Question

a large right triangle is going to be a part of a geometric sculpture, as shown below. the hypotenuse will be 5 feet long. the length of one leg of the triangle is 2 feet less than twice the other leg. find the length of each leg, in feet, and separate them with a comma.

Explanation:

Step1: Apply Pythagorean theorem

$x^{2}+(2x - 2)^{2}=5^{2}$

Step2: Expand the equation

$x^{2}+4x^{2}-8x + 4 = 25$

Step3: Combine like - terms

$5x^{2}-8x+4 - 25=0$
$5x^{2}-8x - 21 = 0$

Step4: Factor the quadratic equation

$(5x + 7)(x - 3)=0$

Step5: Solve for x

$5x+7 = 0$ gives $x=-\frac{7}{5}$; $x - 3=0$ gives $x = 3$. Since length cannot be negative, we take $x = 3$.

Step6: Find the lengths of the legs

One leg is $x = 3$ feet, and the other leg is $2x-2=2\times3 - 2=4$ feet.

Answer:

3,4