Question

The Varners live on a corner lot. Often, children cut across their lot to save walking distance. The diagram to the right represents the corner lot. The children's

path is represented by a dashed line. Approximate the walking distance that is saved by cutting across their property instead of walking around the lot. Hypotenuse 36
Short Leg x
Long Leg x+12
****
The walking distance that is saved by cutting across the lot is how many feet?
(Round the final answer to the nearest integer as needed. Round all intermediate values to the nearest thousandth as needed.)

Answer 1

The distance saved by cutting across the lot is 24 feets

From pythagoras ;

• Hypotenus² = Adjacent² + opposite²

Inputting the parameters into our formula , we have;

36² = x² + (x + 12)²

x² + 12x + 12x + 144

1296 = x² + 24x + 144

x² + 24x - 1152 = 0

Taking 48 and -24 as factors

We have ;

x(x + 48) -24(x + 48)

(x + 48) = 0 or (x - 24) = 0

x = 24 or x = -48

Since, length cannot be negative, then , x = 24.

The sum of the Adjacent and opposite sides;

• 24 + (24 + 12) = 60 feets

The distance saved is ;

• 60 - 36 = 24 feets