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) (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 each of the equal legs. 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. Since $x$ represents a length, we consider the positive square root. So $x=\sqrt{128}=8\sqrt{2}$.
We want to find the system of equations to represent this situation. The equation for the area is $\frac{1}{2}x^{2}=64$ or $y = \frac{1}{2}x^{2}$ and $y = 64$.

Answer:

$y=\frac{1}{2}x^{2}$ and $y = 64$