Question

an isosceles right triangle has legs of length x and an area of 72 square units. which equation can you use to find the length of each leg, x? 72 = x² 72 = 2x² 72 = \frac{1}{2}x² 72² = 2x

Explanation:

Step1: Recall the area formula for a triangle

The area formula for a triangle is \(A=\frac{1}{2}\times base\times height\).

Step2: Identify base and height for the isosceles right - triangle

In an isosceles right - triangle with legs of length \(x\), the base \(b = x\) and the height \(h=x\).

Step3: Substitute into the area formula

Substitute \(b = x\) and \(h = x\) into \(A=\frac{1}{2}\times b\times h\). We get \(A=\frac{1}{2}\times x\times x=\frac{1}{2}x^{2}\).

Step4: Set up the equation

Since \(A = 72\), the equation is \(72=\frac{1}{2}x^{2}\).

Answer:

\(72=\frac{1}{2}x^{2}\) (the third option)