SOLUTION: The longer leg of a right triangle is 4 cm more than four times the length of the shorter leg. The hypotenuse is 1 cm longer than the longer leg. How long are the sides of the tr
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Question 170758This question is from textbook
: The longer leg of a right triangle is 4 cm more than four times the length of the shorter leg. The hypotenuse is 1 cm longer than the longer leg. How long are the sides of the triangle? This question is from textbook
You can put this solution on YOUR website! The longer leg of a right triangle is 4 cm more than four times the length of the shorter leg. The hypotenuse is 1 cm longer than the longer leg. How long are the sides of the triangle?
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Let x = length of shorter leg
then
4x+4 = length of longer leg
4x+5 = length of hypotenuse
.
x^2 + (4x+4)^2 = (4x+5)^2
x^2 + (4x+4)(4x+4) = (4x+5)(4x+5)
x^2 + 16x^2+32x+16 = 16x^2+40x+25
17x^2+32x+16 = 16x^2+40x+25
x^2+32x+16 = 40x+25
x^2-8x+16 = 25
x^2-8x-9 = 0
(x-9)(x+1) = 0
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x = {9, -1}
We can toss out the negative solution leaving:
x = 9 cm (shorter leg)
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Longer leg:
x+4 = 9+4 = 13 cm
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