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show steps pleasethe length of one leg of a right triangle is 7 meters less than the other leg. the length of the hypotenuse is 13 meters. find the lengths of the legs.

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the length of one leg of a right triangle is 7 meters less than the other leg. the length of the hypotenuse is 13 meters. find the lengths of the legs. 

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Step 1

Given that the length of one side in right angle triangle is 7 meters less than the other leg. Suppose the length of side AB is x meter then length of side BC is (x- 7) meter and length of hypotenuse is 13 meter as shown in the below figure

С
13
х-7
А
В
х
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С 13 х-7 А В х

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Step 2

Since ABC is right angle triangle...

AB BC AC2
x2x-7)13
x2x249-14x = 169
2x? -14х — 120 %3D0
x27x 60 0
x2- (12-5)x-60 0
x12x5x -60 = 0
x(х -12) + 5(х —12) — 0
(x5)x12)0
x =-5 orx= 12
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AB BC AC2 x2x-7)13 x2x249-14x = 169 2x? -14х — 120 %3D0 x27x 60 0 x2- (12-5)x-60 0 x12x5x -60 = 0 x(х -12) + 5(х —12) — 0 (x5)x12)0 x =-5 orx= 12

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