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Assoli18 [71]
3 years ago
7

The length of the longer leg of a right triangle is 19ft more than five times the length of the shorter leg. the length of the h

ypotenuse is 20ft more than five times the length of the shorter leg. find the side lengths of the triangle.
Mathematics
1 answer:
dangina [55]3 years ago
7 0
Let x represent the length of the shorter leg.

Longer leg: 5x +19
Hypotenuse: 5x +20

Pythagorean theorem:
.. x^2 +(5x +19)^2 = (5x +20)^2
.. x^2 +25x^2 +190x +19^2 = 25x^2 +200x +20^2 . . . . . . eliminate parentheses
.. x^2 -10x -39 = 0
.. (x -13)(x +3) = 0
.. x = 13 . . . . . . . . . . leg lengths must be positive

The side length of the triangle are 13, 84, 85 feet.
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