Question

The area of a right triangle is 210 inches squared. The height of the right triangle is 35 inches. What is the length of the hypotenuse of the right triangle?

Answer 1

Area of a triangle:

A = b * h / 2


A triangle base is 3 inches more than it's height.

This mean : b = h + 3


A = b * h / 2 = ( h + 3 ) * h / 2 = 35 in ^ 2

( h * h + 3 * h ) / 2 = 35

( h ^ 2 + 3 h ) / 2 = 35 Multiply both sides by 2

h ^ 2 + 3 h = 70 Subtract 70 to both sides

h ^ 2 + 3 h - 70 = 70 - 70

h ^ 2 + 3 h - 70 = 0

The solutions are :

h = - 10

and

h = 7

Height can't be negative so :

h = 7 in

b = h + 3 = 7 + 3 = 10 in


A = 10 * 7 / 2 = 70 / 2 = 35 in ^ 2

Answer 2

X=37 in

Explanation:

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