Question : A rectangular carpet has an area of 120 m2 and a perimeter of 46 m. The length of its diagonal is:
Option 1: 23 m
Option 2: 13 m
Option 3: 17 m
Option 4: 21 m
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Correct Answer: 17 m
Solution : Let the length of the rectangle as $l$ and the width as $w$. The area of the rectangle, $lw = 120\ \text{m}^2⇒l=\frac{120}{w}$ The perimeter of the rectangle, $2(l + w) = 46\ \text{m}$ $⇒l + w = 23$ putting the value of $l$, we get, $\frac{120}{w}+w=23$ $⇒w^2-23w+120=0$ $⇒(w-8)(w-15)=0$ $⇒w=8,15$ If $w=8\ \text{m}$, then $l=15\ \text{m}$ If $w=15\ \text{m}$, then $l=8\ \text{m}$ $\therefore$ The length of the diagonal $= \sqrt{l^2 + w^2}=\sqrt{(8)^2 + (15)^2}= \sqrt{289}=17\ \text{m}$ Hence, the correct answer is 17 m.
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