17.3 Find Unknown Side Lengths


 Gwendolyn Simpson
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1 ? Nme 17.3 Find Unknown Side Lenths ALGEBRA Essentil Question How cn you find the unknown lenth of side in polyon when you know its perimeter? Geometry nd Mesurement 3.7.B MATHEMATICAL PROCESSES 3.1.A, 3.1.F Unlock the Problem Chen hs 27 feet of fencin to put round his rden. He hs lredy used the lenths of fencin shown. How much fencin does he hve left for the lst side? 5 ft 3 ft 7 ft n 4 ft Find the unknown side lenth. Write n eqution for the perimeter. Think: If I knew the lenth of n, I would dd ll the side lenths to find the perimeter. Add the lenths of the sides you know. Think: Addition nd subtrction re inverse opertions. Write relted eqution. So, Chen hs _ feet of fencin left _ + _ + n = n = 27 _ + n = 27 n = _ = Exmple Find unknown side lenths of squre. The squre hs perimeter of 20 inches. Wht is the lenth of ech side of the squre? Think: A squre hs four sides tht re equl in lenth. You cn multiply to find the perimeter. Write multipliction eqution for the perimeter. Use multipliction fct you know to solve. So, the lenth of ech side of the squre is _ inches. Mth Ide A symbol or letter cn stnd for n unknown side lenth. s s s 4 s = 20 4 _ = 20 s Module
2 Exmple Find unknown side lenths of rectnle. 5 ft Luren hs rectnulr blnket. The perimeter is 28 feet. The width of the blnket is 5 feet. Wht is the lenth of the blnket? l Hint: A rectnle hs two pirs of opposite sides tht re equl in lenth. l Add the lenths of the sides you know. _ + _ = _ Subtrct the lenths from the perimeter. 28 _ = _ Divide the difference by 2. 5 ft _ 2 = _ So, the lenth of the blnket is _ feet. Shre nd Show Find the unknown side lenths. 1. Perimeter = 25 centimeters _ + _ + n = 25 n 6 _ + n = 25 3 _ = _ _ n = _ centimeters 2. Perimeter = 34 meters 3. Perimeter = 12 feet j r 7 m 7 m j j = _ meters 558 r r r r = _ feet Mth Tlk Mthemticl Processes Explin how you cn use division to find the lenth of side of squre.
3 Nme Unlock the Problem 4. MultiStep Use Dirms Ltesh wnts to mke border with ribbon round fiure she mde nd sketched t the riht. She will use 44 centimeters of ribbon for the border. Wht is the unknown side lenth? A 3 centimeters C 9 centimeters B 13 centimeters D 6 centimeters h 5. Wht do you need to find? b. How will you use wht you know bout perimeter to help you solve the problem? c. Write n eqution to solve the problem. d. Complete the sentences. The perimeter is _ centimeters. The sum of the sides I know is _ centimeters. A relted subtrction eqution is _ = _ _. So, the lenth of side h is _ centimeters. e. Fill in the bubble for the correct nswer choice bove. 5. MultiStep A rectnle hs perimeter of 34 inches. The left side is 6 inches lon. Wht is the lenth of the top side? Module 17 Lesson 3 559
4 Dily Assessment Tsk Mthemticl Processes Fill in the bubble completely to show your nswer. 6. A wildlife snctury puts fence round section of their lnd. The fence is 19 kilometers lon. Wht is the lenth of the unknown side? 4 km 2 km 4 km A 5 kilometers C 33 kilometers B 7 kilometers D 14 kilometers 4 km n 7. Cir buys piece of ribbon to sew round the edes of squre blnket. She uses 36 inches of ribbon. How lon is ech side of the blnket? A 18 inches C 4 inches B 9 inches D 32 inches 8. MultiStep Kenny puts fence round his 5sided rden. He strts with 35 feet of fencin. After he is done, he hs 5 feet of fencin left over. How lon is ech side of his rden? A 7 feet C 6 feet B 5 feet D 3 feet TEXAS Test Prep Eleni wnts to put fence round her squre rden. The rden hs perimeter of 28 meters. How lon will ech side of the fence be? A B C D 8 meters 7 meters 14 meters 6 meters
5 Homework nd Prctice Nme Geometry nd Mesurement 3.7.B MATHEMATICAL PROCESSES 3.1.A, 3.1.F 17.3 ALGEBRA Find Unknown Side Lenths Find the unknown side lenths. 1. Perimeter = 28 centimeters m 2. Perimeter = 40 feet 11 feet 6 6 m m = _ centimeters = _ feet 11 feet Problem Solvin Use the dirm for Mitch needs to replce the fence in his bckyrd. The dirm shows the lenths of the borders of the fence. The lenth of the fence is 62 meters. Wht is the unknown side lenth? Explin how you will solve the problem. Then write n eqution to solve the problem. 12 m 14 m x 5 m 5 m 7 m 4. Wht if Mitch chnes the shpe of his fence to rectnle? How much fencin will Mitch need? Explin. Module 17 Lesson 3 561
6 Lesson Check TEXAS Test Prep Fill in the bubble completely to show your nswer. 5. Ni hs mirror in the shpe of hexon. He puts frme round it tht hs perimeter of 42 inches. How lon is ech side? A 7 inches C 8 inches B 6 inches D 9 inches 6. Zen hs squre picture frme with perimeter of 28 inches. Which eqution cn she use to find the lenth of ech side? A 4 s = 28 B 4 + s = 28 C D 28 4 = s = s 7. A frmer is puttin new fence round section of his rnch. The fence is 35 kilometers lon. Wht is the lenth of the unknown side? A 6 kilometers x 5 km 8 km B 29 kilometers 7 km C 7 kilometers 9 km D 35 kilometers 8. MultiStep Glend puts border of wllpper round her bedroom wll. The room is rectnle with side lenths of 3 meters nd 4 meters. If she hs 20 meters of wllpper, how much wllpper is left over? 562 A 13 meters C 27 meters B 6 meters D 14 meters 9. MultiStep Jore sews trim round the ede of tblecloth with 8 sides. He hs 32 feet of trim. If ech side of the tblecloth is 2 feet lon, how much trim will Jore hve left? A 10 feet C 42 feet B 8 feet D 16 feet
7 Nme Module 17 Assessment Vocbulry Choose the best term from the box. 1. The distnce round fiure is the. (p. 545) re perimeter Vocbulry Concepts nd Skills Find the perimeter of the fiure. Ech unit is 1 centimeter. q TEKS 3.7.B _ centimeters _ centimeters Find the unknown side lenths. q TEKS 3.7.B 4. Perimeter = 33 centimeters Perimeter = 32 feet 12 ft k 12 ft k = _ centimeters k = _ centimeters 6. Use centimeter ruler to find the perimeter. q TEKS 3.7.B _ centimeters Module
8 Fill in the bubble for the correct nswer choice. 7. Jcob built toolbox with perimeter of 70 inches. Wht is the lenth of side m? q TEKS 3.7.B A B C D 50 inches 20 inches 25 inches 10 inches TEXAS Test Prep m 10 in. 10 in. m 8. Adrienne is decortin squre picture frme. She lued 32 inches of ribbon round the ede of the frme. Wht is the lenth of ech side of the picture frme? q TEKS 3.7.B A 4 inches C 28 inches B 8 inches D 16 inches 9. Wht is the perimeter of the fiure? Ech unit is 1 centimeter. q TEKS 3.7.B A 20 centimeters C 23 centimeters B 18 centimeters D 9 centimeters 10. Jeff is mkin poster for cr wsh for the Cmpout Club. Wht is the perimeter of the poster? q TEKS 3.7.B A 8 feet C 6 feet B 3 feet D 4 feet 3 ft 1 ft 1 ft 3 ft 11. A rectnle hs side lenths of 8 inches nd 10 inches. Wht is the perimeter of the rectnle? q TEKS 3.7.B 564 A 28 inches C 32 inches B 18 inches D 36 inches
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