Question

The hypotenuse of a right triangle is 34 inches. One leg of the triangle is 14 inches less than the other leg. In simplified form, which equation could be used to find the lengths of the legs?

Answer 1

You can use the equation

${(x + 14)}^{2} + {x}^{2} = {34}^{2}$
to find the lenth of the legs

x = leg 1
x + 14 = leg 2

Answer 2

The equation $x^2+14x=480$ could be used to find the length of the legs and this will be determined by using the Pythagorean theorem.

Given :

• The hypotenuse of a right triangle is 34 inches.
• One leg of the triangle is 14 inches less than the other leg.

The Pythagorean theorem can be used to determine the equation used to find the lengths of the legs.

The Pythagorean theorem is given by the formula:

$a^2 + b^2 = c ^2$   --- (1)

Where 'a' is the base, 'b' is the perpendicular and 'c' is the hypotenuse. Now, it is given that the hypotenuse is 34 and one leg of the triangle is 14 inches less than the other leg.

Hypotenuse, c = 14

Base, a = x

Perpendicular, b = x + 14

Now, put the value of a, b, and c in equation (1).

$x^2+(x+14)^2=34^2$

$x^2 +x^2 +28x+196=1156$

$2x^2+28x=960$

$x^2+14x=480$

The equation $x^2+14x=480$ could be used to find the length of the legs.

For more information, refer to the link given below:

https://brainly.com/question/16426393