Question

Triangle MNO is similar to triangle RPO.

Triangle M N O. Side M N is 20 kilometers and side M O is 32 kilometers. Triangle R P O. Side O R is 48 kilometers.

Valek finds the distance between P and R. His work is shown below.

Step 1 StartFraction 32 Over 48 EndFraction = StartFraction 20 Over P R EndFraction

Step 2 20 P R = (32) (48)

Step 3 20 P R = 1,536

Step 4 P R = 76.8 kilometers

What is Valek’s first error?
Valek did not correctly divide 1,536 by 20 going from step 3 to step 4.
Valek did not find the correct product of 32 and 48 going from step 2 to step 3.
Valek should have written the proportion in step 1 as StartFraction 32 Over 20 EndFraction = StartFraction P R Over 48 EndFraction.
Valek should have written the cross-produc

Answer 1

His first error is in Step 2: he cross-multiplied incorrectly. From 32/48 = 20/PR the correct cross-product is 32·PR = 48·20 (not 20·PR = 32·48). Solving 32·PR = 960 gives PR = 30 km.