Question

The width of a rectangle is 6cm less than the length of the rectangle. The perimeter of the rectangle is 72 cm. Write and solve an equation to find the length and width of the rectangle.

Answer 1

The length and width of the rectangle can be determined by setting up the equation for perimeter (P = 2L + 2W), substituting the given values, and solving for L and W. The length (L) is 21 cm, and width (W) is 15 cm.

Step-by-step explanation:

The student is asked to find the length and width of a rectangle given that the width is 6cm less than the length and the perimeter is 72 cm. To solve this:

1. Let the length be L cm, so the width will be L - 6 cm.
2. Write the equation for the perimeter: P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
3. Substitute the expressions for L and W and the given perimeter into the equation: 72 = 2(L) + 2(L - 6).
4. Simplify and solve the equation for L: 72 = 2L + 2L - 12, which simplifies to 72 = 4L - 12, and then 4L = 84, so L = 21 cm.
5. Calculate W by subtracting 6 from L: W = L - 6, so W = 21 - 6, which means W = 15 cm.

The dimensions of the rectangle are 21 cm for the length and 15 cm for the width.