Area and Perimeter Practice Test 1

Here, lb = 120 ${\mathit{m}}^2$
and also, 2 (l + b) = 46
⇒ l + b = 23
Now, l – b = $\sqrt{{\left(\mathit{l}+\mathit{b}\right)}^2-4\mathit{l}\mathit{b}}$
= $\sqrt{{\left(23\right)}^2-4\times 120}$
= $\sqrt{529-480}$
= $\sqrt{49}$ = 7
Since, l = $\frac{1}{2}$ (23 + 7) = 15 m, b = $\frac{1}{2}$ (23 - 7) = 8 m
Hence, diagonal of the carpet = $\sqrt{{15}^2+8^2}$ = $\sqrt{289}$ = 17 m