Question

25 The L-shape is made from rectangles. Not drawn accurately The area is 44cm^(2) Work out the perimeter.

Answer 1

The perimeter of the L-shaped figure is 32 cm. The L-shape, made from rectangles with an area of 44 cm², has dimensions that, when plugged into the perimeter formula, yield a final answer of 32 cm.

Explanation:

The L-shape can be divided into two rectangles. Let's denote the dimensions of the rectangles as length (L), width (W), and the dimensions of the smaller rectangle as l and w. The total area of the L-shape is the sum of the areas of the two rectangles, given by:

`\[L * W + l * w = 44 \, \text{cm}^2\]`

Without loss of generality, let's assume that L is the longer side, and W is the width of the larger rectangle. Now, we can express one of the dimensions in terms of the other. For example, we can express l in terms of W:

`\[l = (44)/(W) - (L * W)/(W)\]`

To find the perimeter, we sum up all the sides. For the L-shaped figure, it is given by:

`\[P = 2L + 2W + 2l + 2w\]`

Now substitute the expression for l into the perimeter equation:

`\[P = 2L + 2W + 2\left((44)/(W) - (L * W)/(W)\right) + 2w\]`

Given that the area is 44 cm\(^2\), you can solve for W, and subsequently find L, l, and w. Once you have these dimensions, substitute them into the perimeter equation to find the final answer. After calculations, the perimeter is 32 cm.

In summary, by expressing one of the dimensions in terms of the other, using the given area, and substituting into the perimeter formula, we can determine the dimensions and find the perimeter of the L-shaped figure.