# The hypotenuse of a triangle is 26 feet long. One leg of the triangle is 14 feet longer than the other leg. What are the lengths of the legs of the triangle?

Mar 20, 2018

The two lengths are 10 feet and 24 feet.

#### Explanation:

By Pythagoras Theorem, ${a}^{2} + {b}^{2} = {c}^{2}$ .
Since the hypotenuse, c is 26 feet long, ${26}^{2}$ = 676.
${10}^{2}$+ ${24}^{2}$ = 676.
Hence the answer is 10 feet and 24 feet.

Mar 20, 2018

Lengths of the legs are $10 \mathmr{and} 24$ ft

#### Explanation:

Let length of one leg of the triangle be $x$ ft , then other leg will

be x+14 ; h= 26 ft . We know ${h}^{2} = {x}^{2} + {\left(x + 14\right)}^{2}$ or

${26}^{2} = {x}^{2} + {\left(x + 14\right)}^{2} \mathmr{and} {x}^{2} + {x}^{2} + 28 x + 196 = 676$ or

$2 {x}^{2} + 28 x - 480 = 0 \mathmr{and} {x}^{2} + 14 x - 240 = 0$ or

${x}^{2} + 24 x - 10 x - 240 = 0$ or

$x \left(x + 24\right) - 10 \left(x + 24\right) = 0 \mathmr{and} \left(x + 24\right) \left(x - 10\right) = 0$

Either $x + 24 = 0 \therefore x = - 24 \mathmr{and} x - 10 = 0 \therefore x = 10$

leg can not be negative so, $x = 10 \therefore x + 14 = 10 + 14 = 24$

Hence lengths of the legs are $10 \mathmr{and} 24$ ft . [Ans]