The length of a rectangle is twice its width.If the perimeter of the rectangle is 54 yd, find its area.

Sure, let's solve this step by step.

Step 1: Let's denote the width of the rectangle as x. Therefore, the length of the rectangle is 2x (since it's twice the width).

Step 2: The formula for the perimeter of a rectangle is P = 2l + 2w, where l is the length and w is the width. We know that the perimeter is 54 yd, so we can set up the equation: 54 = 2(2x) + 2x.

Step 3: Simplify the equation: 54 = 4x + 2x.

Step 4: Combine like terms: 54 = 6x.

Step 5: Solve for x: x = 54 / 6 = 9 yd. So, the width of the rectangle is 9 yd.

Step 6: Find the length by multiplying the width by 2: 2 * 9 = 18 yd. So, the length of the rectangle is 18 yd.

Step 7: Now that we have the length and the width, we can find the area of the rectangle using the formula A = lw, where A is the area, l is the length, and w is the width. So, A = 18 * 9 = 162 square yd.

So, the area of the rectangle is 162 square yards.