Question

A rectangular piece of paper has an area of 24 square inches. You trim the paper so that it fits into a square frame by trimming 3 inches from the length and 1 inch from the width of the paper. Write and solve an equation to find the side length of the resulting square paper.

Answer 1

Length of the square = 3 inches

Equation:
`l = L - 3` and
`l = W - 1`

Explanation:

Given

Area of the rectangle = 24

Required

Length of the square when the dimension of the rectangle is trimmed by 3 inches * 1 inches

Represent the dimension on the rectangle by L and W

Such that L represent Length and W, Width

This implies that

`L * W = 24`

Represent the length of the rectangle by l

Such that

`l = L - 3` and
`l = W - 1` (When trimmed)

Equate both expressions

`L - 3 = W - 1`

Add 3 to both sides

`L - 3 + 3 = W - 1 + 3`

`L = W + 2`

Next is to list all possible dimensions of the rectangle;

`Area(L,W) = Length * Width`

`Area(24,1) = 24 * 1 = 24`

`Area(12,2) = 12 * 2 = 24`

`Area(8,3) = 8 * 3 = 24`

`Area(6,4) = 6 * 4 = 24`

From the list above, the only calculation that fits our solution is

`Area(6,4) = 6 * 4 = 24`

Such that

`6 = 4 + 2`

By direct comparison of
`6 = 4 + 2` to
`L = W + 2`;

`L = 6`

`W = 4`

Recall that

`l = L - 3` and
`l = W - 1`

Substitute 6 for L and 4 for W

`l = 6 - 3` and
`l = 4 - 1`

`l = 3` in both cases

Hence, the length of the square is 3 inches

And the equation is
`l = L - 3` and
`l = W - 1`