Question

7. Jason wants to walk the shortest distance to get from the parking lot to the beach

Answer 1

There are 3 right triangles.
                         Long leg          short leg           hypotenuse
Large                  ?                          ?                       32+18 = 50 m
Medium            32 m                     x                          ?
Small                   x                         18 m                    ?

Similar triangles: small & medium

short leg / long leg
x/32 = 18/x
x*x = 18 * 32
x² = 576
√x² = √576
x = 24

                       Long leg          short leg           hypotenuse
Large                  ? → 40 m          ?                       32+18 = 50 m
Medium            32 m                     24 m                 ? → 40 m
Small                24 m                     18 m                  ? → 30 m

solve hypotenuse of medium and small using Pythagorean theorem.

32² + 24² = c²
1024 + 576 = c²
1600 = c²
√1600 = √c²
40 = c

24² + 18² = c²
576 + 324 = c²
900 = c²
√900 = √c²
30 = c

Solve for the long leg of the large right triangle using ratio and proportion
medium and large: long leg / hypotenuse

32/40 = x/50
32*50 = 40 * x
1600 = 40x
1600/40 = x
40 = x

A. How far is the spot on the beach from the parking lot? 24 meters

B. How far will he have to walk from the parking lot to get to the refreshment stand? 40 meters