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EXAMPLE 3

First draw triangle QRS in a coordinate plane. Find the side lengths. Use the Distance Formula to find QR and RS. EXAMPLE 3. Standardized Test Practice. SOLUTION. QS. 5 – 1. 4 units. =. =. (5 – 4) + (2 – 6). (4 – 1) + (6 – 2). QR. 25. 11. 5 units. 2. 2. 2. 2. =. =. =. RS.

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EXAMPLE 3

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  1. First draw triangle QRSin a coordinate plane. Find the side lengths. Use the Distance Formula to find QRand RS. EXAMPLE 3 Standardized Test Practice SOLUTION

  2. QS 5 – 1 4 units = = (5 – 4) + (2 – 6) (4 – 1) + (6 – 2) QR 25 11 5 units 2 2 2 2 = = = RS 4.1 units = = P QS + QR + RS 4 + 5 + 4.1 13.1 units = = The correct answer isC. ANSWER EXAMPLE 3 Standardized Test Practice Then find the perimeter.

  3. Skating Rink An ice-resurfacing machine is used to smooth the surface of the ice at a skating rink. The machine can resurface about 270 square yards of ice in one minute. EXAMPLE 4 Solve a multi-step problem About how many minutes does it take the machine to resurface a rectangular skating rink that is 200 feet long and 90 feet wide? SOLUTION The machine can resurface the ice at a rate of 270square yards per minute. So, the amount of time it takes to resurface the skating rink depends on its area.

  4. STEP 1 Find the area of the rectangular skating rink. Area = lw = 200 (90) = 18,000 ft 2 The resurfacing rate is in square yards perminute. Rewrite the area of the rink insquareyards. There are 3 feet in 1yard, and 32 = 9 square feet in 1 square yard. 18,000 ft 2 = 1 yd 2 2000 yd 2 9 ft 2 EXAMPLE 4 Solve a multi-step problem Use unit analysis.

  5. Write a verbal model to represent the situation. Then write and solve an equation based on the verbal model. STEP 2 2000 270 t = 7.4 t It takes the ice-resurfacing machine about 7 minutes to resurface the skating rink. ANSWER EXAMPLE 4 Solve a multi-step problem Let trepresent the total time (in minutes) needed to resurface the skating rink. Substitute. Divide each side by 270.

  6. 4. Describe how to find the height from Fto EGin the triangle at the right. The height is the length of the segment from point F to EG at the point (1,3) using the coordinate grid to count units , the height is 6 ANSWER for Examples 3 and 4 GUIDED PRACTICE

  7. 5. Find the perimeter and the area of the triangle shown at the right. (7 – 1)2 + (3 – 2)2 (1 – 7)2 + (6 – 3)2 (2 – 6)2 + (1 – 1)2 37 45 EG = = 4 units FG 6.1 units = = = FG 6.7 units = = = for Examples 3 and 4 GUIDED PRACTICE SOLUTION Use the distance formulas to count EG, FG and EF

  8. 4 + 6.1 + 6.7 = 16.8 P = EG + FG + EF = Area = 6 4 = 12 Perimeter is 16.8 units and area is12 units. ANSWER 1 2 for Examples 3 and 4 GUIDED PRACTICE Then find the perimeter Substitute 6 for height and 4 for base

  9. Find the area of the rectangular skating ring. STEP 1 What if ? In Example 4, suppose the skating rink is twice as long and twice as wide. Will it take an ice-resurfacing machine twice as long to resurface the skating rink? Explain your reasoning. 6. 1yd2 72000 ft2 = 8000 yd2 9ft2 for Examples 3 and 4 GUIDED PRACTICE Area = lw = 400 (180) = 72000ft2 The resurfacing rate is in square yards per minute rewrite the area of the ring in square yards. There are 3 feet in 1 yard ,and 32 = 9 square feet in square yard . Use unit analysis

  10. STEP 2 Let t represent the total time (in minutes) needed to surface the skating ring. Area of ring = resurfacing rate Total time X (yd2per min) (min) 8000 = 270 t t 29.6 No; the new area is more than twice as big and it takes about four times as long as to resurface the skating ring. ANSWER for Examples 3 and 4 GUIDED PRACTICE Substitute Divide each side by 270

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