Question

The hypoténuse of a right triangleis 34 in. One leg of the triangle is 14 inches less than the other leg. In simplified form, which equation could be used to find the lengths of the leg

Answer 1

Answer: the length of one leg is 30 inches and the leg of the other leg is 16 inches.

Step-by-step explanation:

Let the other leg of the triangle be x inches.

One leg of the triangle is 14 inches less than the other leg. This means that the length of this leg of the triangle is (x-14) inches.

The length of the hypothenuse of the right triangle is 34 inches.

The diagram of the triangle, showing it's dimensions is shown in the attached photo.

Applying Pythagoras theorem,

Hypothenuse^2 = adjacent^2 + opposite ^2

The simplified equation that can be used to find the lengths of the legs is

34^2 = (x-14)^2 + x^2

1156 = (x-14)(x-14) + x^2

1156 = x^2 - 14x - 14x + 196 + x^2

1156 = 2x^2 -28x +196

2x^2 -28x +196 - 1156 = 0

2x^2 -28x - 960 = 0

Dividing through by 2,

x^2 -14x - 480 = 0

x^2 +16x - 30x - 480 = 0

x(x+16)-30(x+16) = 0

(x + 16)(x - 30) = 0

x+16 = 0 or x-30= 0

x = -16 or x = 30

So x = 30 inches( because it cannot be negative)

One leg = x-14 = 30-14 = 16 inches