Length of one Leg of a Triangle

Question

The length of one leg of a right triangle is 7 ft longer than the other leg. The hypotenuse is 17 ft long. Find the lengths of the two legs.

Show your work

Answer 1

Hi Jim,

We would use the pythagorean theorem.

One leg would be x

the other is x + 7

hypotenuse is 17.

so x^2 + (x +7 )^2 = 17^2

solving x^2 + x^2 + 14 x + 49 = 289

solving our quadratic would be

2 x ^ 2 + 14 x + -240= 0

factoring x = 8

and x + 7 =15

I hope this helps

Answer 2

Since its a right angled triangle, it will satisfy the Pythagoras equation.

The sum of the squares of the sides is equal to the square of the hypotenuse.

If one side is x, the other side is 7+x.

so x² + (7+x)² = 17²

x² + x² + 14x + 49 = 289

2x² + 14x - 240 = 0.

x² + 7x - 120 = 0.

x = (-7 + √(49 + 4*1*120))/2 or (-7 - √(49 + 4*1*120))/2

x = 8, -15

Since negative side of a triangle is not acceptable, the length of other two legs are 8 ft and 15 ft