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

Answer:

Length of the square = 3 inches

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

Step-by-step 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 $l = W - 1$