The length of the rectangle is $(4 a b + 6) m$ and breadth of the rectangle is $(6 b^{2} + 2 a b) m$ . Find the area of the rectangle.

(24 a b^{3} + 18 a^{2} b^{2} + 36 b^{2} + 12 a b) m^{2}

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(24 a b^{3} + 6 a^{2} b^{2} + 6 b^{2} + 12 a b) m^{2}

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(24 a b^{3} + 8 a^{2} b^{2} + 36 b^{2} + 12 a b) m^{2}

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(8 a^{2} b^{2} + 36 b^{2} + a b) m^{2}

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Solution

The correct option is C $(24 a b^{3} + 8 a^{2} b^{2} + 36 b^{2} + 12 a b) m^{2}$
Given:
Length of the rectangle
$= (4 a b + 6) m$

Breadth of the rectangle
$= (6 b^{2} + 2 a b) m$

Area of a rectangle = length $\times$ breadth
$= (4 a b + 6) \times (6 b^{2} + 2 a b)$
$= 4 a b \times 6 b^{2} + 4 a b \times 2 a b + 6 \times 6 b^{2} + 6 \times 2 a b)$
$= (24 a b^{3} + 8 a^{2} b^{2} + 36 b^{2} + 12 a b) m^{2}$

Suggest Corrections

Similar questions

(6 b^{2} + 2 a b)

a = 2

b = 1.

(4 a b + 6) m

(6 b^{2} + 2 a b) m

6 b^{2}

24 a^{2} b^{2}

24 a b^{3}

24 a b^{2}

24 a b

= 102

= 6

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