the hypotenuse of an isosceles right triangle is 9cm longer than either of is legs.find the EXACT length length of each side

Question

the hypotenuse of an isosceles right triangle is 9cm longer than either of is legs.find the EXACT length length of each side

Answer 1

Hi Darlene, I agree with your answer up to the roots that are different than the ones you present, please take a look at your three last steps. 

L² + L² = (L+9)²

2L²=L² + 18L + 81

L² - 18L - 81 = 0

L1= 21.73 m

The other root is negative and the answer is not common sense.

Answer 2

Hi, Claudia!

 

Start with the formula that relates the sides of a right triangle...

 

(leg)² + (leg)² = (hyp)²

 

Let's call the leg x. The hypotenuse would then by x + 9. So...

 

x² + x² = (x + 9)²

2x² = x² + 18x + 81

x² - 18x - 81 = 0

(x - 9)(x - 9) = 0

x = 9

 

:)