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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