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The longer leg of a right triangle is $1$ foot shorter than twice the length of the shorter leg. The area of the triangle is $60$ square feet. What is the length of the hypotenuse, in feet?

 Jun 12, 2020
 #1
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so when the area of the triangle is 60 the 2 bases multiplied by each other equals 120 since 60*2 and we get the equation (2x^2-x)=120 and 2x^2=120+x so x=8 and 8*2-1=17 and 8^2+17^2=353 so the hypotenuse is \(\sqrt{353}\)

 Jun 12, 2020
 #2
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 8*2-1=17    wrong!!!

 

Another way to calculate an 'x'       1/2 [ x (2x-1)] = 60 smiley

Guest Jun 12, 2020
 #3
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The longer leg of a right triangle is $1$ foot shorter than twice the length of the shorter leg. The area of the triangle is $60$ square feet. What is the length of the hypotenuse, in feet?

 

Short way:

Hypotenuse     c = sqrt ( A * 2 ) = sqrt ( 60*2 )  smiley

Guest Jun 12, 2020

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