Exponents and Polynomials

Question

The length of the longer leg of a right triangle is 25ft more than seven times the length of the shorter leg. The length of the hypotenuse is 26 ft more than seven times the length of the shorter leg. Find the side lengths of the triangle.

Length of the shorter leg: ft

Length of the longer leg: ft

Length of the hypotenuse: ft

Answer 1

The legs are x, 7x + 25, 7x + 26

x² + (7x + 25)² = (7x + 26)²

x² - 14x - 51 = 0

{-3, 17}

The -3 does not apply to Geometry

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Answer 2

shorter leg = 17 feet

longer leg = 144 feet

hypotenuse =145 feet

145^2 = 144^2 +17^2

145 = 26+7(17)

144 = 25 +7(17)

there is a 2nd possible solution but with legs of negative length

longer leg =4

shorter leg = -3

hypotenuse = 5

5^2 = (4)^2 + (-3)^2= 16+9

5=26 +7(-3) = 26-21 =5

4 = 25 +7(-3) - 25-21 = 4

if a negative leg is allowed, such as maybe to indicate direction, then there are two possible solutions.

or in a very non-Euclidian or twilight zone geometry