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Find the length of the shorter leg of a right triangle with the longer leg is 9 feet more than the shorter leg the hypotenuse is nine feet less than twice the shorter leg

User DamianFox
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1 Answer

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Answer:

Length of Shorter leg = 27 feet

Length of Longer leg = 36 feet

Length of Hypotenuse = 45 feet

Explanation:

Given:

Let,

Length of Shorter leg = x,

According to the given condition we have

∴ Length of Longer leg = x + 9 feet

∴ Length of Hypotenuse = 2x - 9 feet

To Find:

Length of Shorter leg = ?

Solution:

Now In Right Angle Triangle, By Pythagoras theorem we have


(\textrm{Hypotenuse})^(2) = (\textrm{Shorter leg})^(2)+(\textrm{Longer leg})^(2)

substituting the given values we get


(2x-9)^(2) = (x)^(2)+(x+9)^(2)\\

By using Identity (A ± B)² = A² ± 2AB +B² we get


4x^(2) -36x+81=x^(2) +(x^(2) +18x+81)\\\\4x^(2) -2x^(2) -36x-18x=81-81\\\\2x^(2) -54x=0\\2x(x-27)=0\\2x=0 or x-27=0\\\therefore x\ cannot\ be \ zero\\\therefore x = 27 \feet

Substituting x=27 we get

∴ Length of Longer leg = x + 9 =27 +9 = 36 feet

∴ Length of Hypotenuse = 2x - 9 = 2×27 -9 = 45 feet

User Kalkin
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