Danielle H.
asked • 02/05/23exponents and polynomials using the pythagorean theorem
the longer leg of a right triangle is 7 cm longer than the shorter leg. the hypotenuse is 9 cm longer than the shorter leg. find the sides lengths of the triangle.
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1 Expert Answer
Robert K. answered • 02/05/23
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Let X = length of shorter leg, cm
X + 7 = length of longer leg, cm
X + 9 = length of hypotenuse, cm
X^2 + (X + 7)^2 = (X + 9)^2
X^2 + X^2 + 14X+ 49 = x^2 + 18X + 81
X^2 - 4X - 32 = 0
(X - 8)(X + 4) = 0
X = 8 and X = -4
The negative answer is rejected and we take X = 8 cm for the shorter leg.
X = 8 + 7 = 15 cm for the longer leg.
X = 8 + 9 = 17 cm for the hypotenuse.
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Patrick F.
First draw a right triangle. Then label it. Each side will be labeled in terms of the shorter side (you could call the shorter side x). Finally use pythagoras to set up an equation, solve for x, then give all three sides. Give it a go! If you get stuck, post your work and we'll give you some guidance.02/05/23