Question

A rectangular carpet has area 120 m² and perimeter 46 metres. The length of its diagonal is

(a) 15 m
(b) 16 m
(c) 17 m
(d) 20 m

Answer 1

(c) 17 m
Area of the rectangle = 120 m²
Perimeter = 46 m
Let the sides of the rectangle be l and b.
Therefore
Area = lb = 120 m² ...(1)
Perimeter = 2 (l + b) = 46
or, ( l + b ) = $\frac{46}{2}$ = 23 m ...(2)
Now, length of the diagonal of the rectangle = $\sqrt{\left(l^{\mathit{2}\mathit{}}+b^{\mathit{2}}\right)}$
So, we first find the value of (l² + b²)
Using identity:
(l² + b² ) = (l + b)² $-$ 2 (lb) [From (1) and (2)]
Therefore
(l² + b²) = (23)² $-$ 2 (120)
= 529 $-$ 240 = 289
Thus, length of the diagonal of the rectangle = $\sqrt{\left(l^{\mathit{2}\mathit{}}+b^{\mathit{2}}\right)}$ = $\sqrt{289}$ = 17 m