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: Analyze the area formula

The area of a right - isosceles triangle with leg length \(x\) is \(A=\frac{1}{2}x^{2}\). Let \(y\) represent the area. So \(y = \frac{1}{2}x^{2}\).

Step2: Set up the system

We know the area \(y = 64\). So the system of equations is formed by equating the two expressions for \(y\).

Answer:

The system \(y=\frac{1}{2}x^{2}\) and \(y = 64\) can be used.