Question

sun shades are sold in the shape of right isosceles triangles. if the equation represents one shade that shields 64 square feet of area, which system can be used to find the lengths of the legs of the sun shade? (\frac{1}{2}x^{2}=64). use the graphing calculator to graph the system. the solutions to the system are. since the side lengths of a triangle must be positive, the length of one leg of the sun shade is feet. y = (\frac{1}{2}x^{2}+64) and y = (\frac{1}{2}x^{2}-64), y = (\frac{1}{2}x^{2}) and y = 64, y = (\frac{1}{2}x^{2}+64) and y = 0

Explanation:

Step1: Recall area formula for right - isosceles triangle

The area formula for a right - isosceles triangle is $A=\frac{1}{2}x^{2}$, where $x$ is the length of a leg. Given $A = 64$, so $\frac{1}{2}x^{2}=64$.

Step2: Solve the equation for $x$

Multiply both sides of the equation $\frac{1}{2}x^{2}=64$ by 2 to get $x^{2}=128$. Then take the square - root of both sides: $x=\pm\sqrt{128}=\pm8\sqrt{2}$.

Step3: Select the positive solution

Since the length of a side of a triangle cannot be negative, we take the positive value of $x$. So $x = 8\sqrt{2}\approx11.31$ feet.

Answer:

$8\sqrt{2}\approx11.31$ feet