Triangle Problem

Question

The longer side of a right triangle is 28 units long. The perimeter of the triangle is the geometric mean of 4 and 900. Find the length of the other side and the hypotenuse of the triangle. 

Answer 1

 

Hi Chris,

 

The given conditions include

 

     a) The longer side = 28 units long, and

 

     b) The perimeter = √(4·900) = 60 units long.

 

If x and y denote the length of the shorter side and that of hypotenuse, respectively,

we get

 

     x + y + 28 = 60     (Eq. 1)

 

     x² + 28² = y²     (Eq. 2, from the Pythagorean Theorem)

 

By solving the system of Eq. 1 and Eq. 2, we get

 

     x = 3.75     and     y = 28.25

 

 

∴ The length of the shorter side is 3.75 units long, and

 

   the length of the hypotenuse is 28.25 units long.