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 = 0 \\)
\\( y = \frac { 1 } { 2 } x ^ { 2 } \\) and \\( y = 64 \\)
\\( y = \frac { 1 } { 2 } x ^ { 2 } + 64 \\) and \\( y = \frac { 1 } { 2 } x ^ { 2 } - 64 \\)

Explanation:

Step1: Recall the area formula for a right - isosceles triangle

The area formula for a right - isosceles triangle with legs of length \(x\) is \(A=\frac{1}{2}x^{2}\). We are given that \(A = 64\).

Step2: Set up the system of equations

Let \(y=\frac{1}{2}x^{2}\) (the area formula as a function of \(x\)) and \(y = 64\) (the given area value).

Answer:

\(y=\frac{1}{2}x^{2}\) and \(y = 64\) (the second option)