Chapter 4, Problem 40CLR

To determine

To Find: the dimensions of the rectangle in pieces are cut to make square.

Answer to Problem 40CLR

  $15\text{cm}\times 13\text{cm}$

Explanation of Solution

Given:

  $4\text{cm}$ strip is cut off top and $2\text{cm}$ from one side.

Area of original is $74{\text{cm}}^2$ greater than the area of square.

Calculation:

Let $L$ be the length of rectangle and $W$ be width.

Dimension of square is.

  $\left(L-4\right)\times \left(W-2\right)$

Since, length is equal to the width in a square therefore.

  $\begin{array}{l}\left(L-4\right)=\left(W-2\right)\\ L=W-2+4\\ L=W+2\end{array}$

Apply area condition.

  $\begin{array}{l}\text{Area of Rectangle-Area of Square=74}\\ LW-\left(L-4\right)\times \left(W-2\right)=74\\ \left(W+2\right)W-\left(W+2-4\right)\left(W-2\right)=74\\ W^2+2W-\left(W-2\right)\left(W-2\right)=74\\ W^2+2W-\left(W^2-2W-2W+4\right)=74\\ W^2+2W-\left(W^2-4W+4\right)=74\\ 6W=78\\ W=13\end{array}$

Length of rectangle is.

  $\begin{array}{l}L=W+2\\ L=13+2\\ L=15\end{array}$

Therefore, the answer $15\text{cm}\times 13\text{cm}$ .