The areas of a square and a rectangle are equal. The length of the rectangle is greater than the length of a side of the square by $5 c m$ and breadth is less than the side of the square by $3 c m$ . The perimeter of the rectangle is

17 c m

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26 c m

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30 c m

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34 c m

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Solution

The correct option is A $34 c m$
Let each side of the square be 1em, Then, $(l + 5) (l - 3) = l^{2}$
$\Rightarrow l^{2} + 2 l - 15 = l^{2} \Rightarrow 2 l = 15 \Rightarrow l = 7.5$
$∴$ Length of the rectangle $= 7.5 + 5 = 12.5 c m$
Breadth $= 7.5 - 3 = 4.5 c m$
$∴$ Perimeter $= 2 (12.5 + 4.5) c m = 34 c m$ .

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The areas of a square and a rectangle are equal. The length of the rectangle is greater than the length of a side of the square by 5 cm and breadth is less than the side of the square by 3 cm. The perimeter of the rectangle is

The correct option is A 34 cmLet each side of the square be 1em, Then, (l+5)(l−3)=l2⇒l2+2l−15=l2⇒2l=15⇒l=7.5∴ Length of the rectangle =7.5+5=12.5 cmBreadth =7.5−3=4.5 cm∴ Perimeter =2(12.5+4.5) cm=34 cm.

The areas of a square and a rectangle are equal. The length of the rectangle is greater than the length of a side of the square by $5 c m$ and breadth is less than the side of the square by $3 c m$ . The perimeter of the rectangle is