Question

the shorter leg of a right triangle is 8 inches shorter ybsn the longer leg. the hypotenuse is 8 inches longer thsn the longer leg​

Answer 1

Answer:

Short leg = 24inches

Long leg = 32inches

Hypotenuse = 40inches

Step-by-step explanation:

Given:

• shorter leg is 8inches shorter than the longer leg
• hypotenuse is 8inches longer than the longer leg
• longer leg = x inches

Pythagorean Theorem:

a²+b²=c² → (x-8)²+ x² = (x+8)²

Solving for both sides:

x² - 16x+ 64 + x² = x²+ 16x + 64

More Painful Solving:

x² - 32x = 0

x(x-32) = 0

 

x=0 or 32

Can't use the 0 so we trash it!

x=32

add 8 to get the hypotenuse and subtract 8 to get the short leg