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? a. 2x² - 28x = 960 b. 2x² - 28x = 1176 c. 2x² - 14x = 34 d. x² + 14x = 960

Explanation:

Step1: Let the longer leg be $x$ inches.

The shorter leg is $x - 14$ inches.

Step2: Apply Pythagorean theorem.

In a right - triangle, $a^{2}+b^{2}=c^{2}$, where $c = 34$ (hypotenuse), $a=x$ and $b=x - 14$. So $x^{2}+(x - 14)^{2}=34^{2}$.

Step3: Expand the equation.

$x^{2}+x^{2}-28x + 196=1156$.

Step4: Combine like terms.

$2x^{2}-28x+196 - 1156=0$, which simplifies to $2x^{2}-28x - 960 = 0$. Divide through by 2 gives $x^{2}-14x - 480=0$. Multiply through by 2 again to get $2x^{2}-28x=960$.

Answer:

A. $2x^{2}-28x = 960$