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

Let x = length of the shorter leg.

Then length of longer leg = 7x + 25 and length of hypotenuse = 7x + 26

By the Pythagorean Theorem, x² + (7x + 25)² = (7x + 26)²

x² + 49x² + 350x + 625 = 49x² + 364x + 676

So, x² - 14x - 51 = 0

Solve for x.

Answer 2

h=26+7S

L=25+ 7S

7S=L-25

S = (L-25)/7

L-h = -1

h=L+1

h^2 = L^2 -2L+1

h= 26+7S = 26+L-25= L+1

h^2 =L^2 + S^2 = L^2 + [(L-25)/7]^2

L^2 +2L+1 = L^2 + (L^2 -50L + 625)/49

98L +49 = L^2 -50L +625

L^2 - 148L + 576 = 0

L = 148/2 +/-(1/2)sqr(148^2 -4(576))

L = 74 +/- 70= 4 or 144

h = 145

S = sqr(145^2-144^2) = 17

sides are 17, 144 and 145

145 = 26+7(17)=26+119

144 = 25+7(17) = 25+119

145^2 = 144^2 +17^2

21025= 20736+289

longer side = 144 feet

shorter side = 17 feet

hypotenuse = 145 feet