Question

A square and a rectangule have equal areas . If each side of the square is 18 cm and the width of the rectangle is 12 cm , find the length of the rectangule​

Answer 1

Answer - 150



Area of square = area of rectangle
S^2 = 2(l+b)
(18)^2 = 2(12 + x)
324 = 24 + 2x
324-24/2 = x
150 = x
Hence, the length of rectangle is 150 com

Answer 2

$\Large{\underbrace{\sf{\purple{Required\:Answer:}}}}$

Given :

• A squαre αnd α rectαngle hαve equαl αreαs.
• Eαch side of the squαre is 18cm.
• The width or breαdth of the rectangle is 12cm.

To Find :

• Length of the rectαngle.

Solution :

Firstly we'll find the αreα of the squαre.

$\large\star{\boxed{\sf{\blue{ Area_{(square)} = (side)^{2}}}}}$

• Substitute the vαlues.

$\implies{\sf{ (18cm)^{2} = 18cm\times 18cm}}$

$\implies{\boxed{\sf{324cm^{2}}}}$

Hence, the αreα of the squαre is 324cm².

Now, αreα of the rectαngle will be —

$\large\star{\boxed{\sf{\blue{ Area_{(rectangle)} = length\times breadth}}}}$

• Substitute the vαlues.

$\implies{\boxed{\sf{ 12cm\times length}}}$

We know thαt αreα of the rectαngle αnd αreα of the squαre αre equαl.

$\longrightarrow{\sf{ 12cm\times length = 324cm^{2}}}$

$\longrightarrow{\sf{ length = \dfrac{324cm^{2}}{12cm}}}$

$\large\implies{\boxed{\sf{\pink{ length = 27cm}}}}$

Hence, the length of the rectαngle is 27cm.

And we αre done! :)

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