EXAMPLE 3 Standardized Test Practice SOLUTION First draw

EXAMPLE 3 Standardized Test Practice SOLUTION 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 QS = 5 – 1 = 4 units 2 2 QR = (4 – 1) + (6 – 2) RS = (5 – 4) + (2 – 6) = 25 = 5 units = 11 4. 1 units Then find the perimeter. P = QS + QR + RS ANSWER 4 + 5 + 4. 1 = 13. 1 units The correct answer is C.

EXAMPLE 4 Solve a multi-step problem 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. 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 270 square yards per minute. So, the amount of time it takes to resurface the skating rink depends on its area.

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

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

GUIDED PRACTICE 4. for Examples 3 and 4 Describe how to find the height from F to EG in the triangle at the right. ANSWER 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

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

GUIDED PRACTICE for Examples 3 and 4 Then find the perimeter P = EG + FG + EF = 4 + 6. 1 + 6. 7 = 16. 8 Area = 1 2 ANSWER 6 4 = 12 Substitute 6 for height and 4 for base Perimeter is 16. 8 units and area is 12 units.

GUIDED PRACTICE 6. for Examples 3 and 4 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. STEP 1 Find the area of the rectangular skating ring. Area = lw = 400 (180) = 72000 ft 2 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. 1 yd 2 2 72000 ft 9 ft 2 = 8000 yd 2 Use unit analysis

GUIDED PRACTICE for Examples 3 and 4 STEP 2 Let t represent the total time (in minutes) needed to surface the skating ring. Area of ring = resurfacing rate X (yd 2 per min) 8000 = 270 29. 6 ANSWER t t Total time (min) Substitute Divide each side by 270 No; the new area is more than twice as big and it takes about four times as long as to resurface the skating ring.