abigailnsears
Answered

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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​

Sagot :

ExoticHypo

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

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