Question

A right triangle has legs with lengths equal to 10 inches and 9x inches. Its hypotenuse measures (x + 10) inches. What is the approximate value of the hypotenuse?

Answer 1

Answer with Step-by-step explanation:

Given: A right triangle whose legs has lengths equal to 10 inches and 9x inches and Its hypotenuse measures (x + 10) inches.

According to the pythagoras theorem, sum of square of the legs of a right angle triangle equals the square of hypotenuse.

so, 10²+(9x)²=(x+10)²

i.e. 100+81x²=x²+100+20x

      80x²-20x=0

   20x(4x-1)=0

so, either x=0 or x=1/4

x=0 is not possible since length of one leg is 9x and it can't be zero

Hence, x=1/4 i.e. x+10=10+1/4

                                  = 10.25

so, approximate length of hypotenuse=10.25 inches

Answer 2

The approximate value of the hypotenuse is 10.25 seconds