Chapter 11.7, Problem 6PSA

To determine

To check: Whether G succeeds or not in making the size of the garden twice as large.

Answer to Problem 6PSA

No, she did not succeed in making the size of the garden twice as large.

Explanation of Solution

Given Information:

Side of a square garden $\left(a\right)=3$ m.

Formula used:

Area of a rectangle ( A₁ ) = length $\times$ breadth $=l\times b$

Where

  $"l"$ is the length of the rectangle

  $"b"$ is the breadth of the rectangle

Area of a square $\left(A_2\right)=$ $sid{e}^2$ $=a^2$

Calculation:

We know that the garden is in the shape of the square.

Therefore, the area of the garden will be given as follows:

  $A_1=a^2$ … (Where $a=3$ m is the side of the garden)

  $\begin{array}{l}{A}_1=3^2\\ A_1=9{\text{ m}}^2\end{array}$

Now, G wishes to double the size of the garden.

This means, new area of the garden

  $\left(N_1\right)=2\times 9{\text{ m}}^2=18{\text{m}}^2\mathrm{...}(\text{i})$

G decides to double the length and double the breadth.

New length $\left(l_1\right)=2\times 3\text{m}=6\text{m}$

New breadth $\left(b_1\right)=2\times 3\text{m}=6\text{m}$

Now, $N_1$ = area of a rectangle having length 6m and breadth 6m

  $N_1=6\text{m}\times 6\text{m}=36{\text{m}}^2$ … (ii)

From (i) and (ii), we get that the two areas are not equal.

Hence, G did not succeed in making the size of the garden twice as large by doubling the length and the breadth.