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?

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