1.

The area of a square of side 18 cm is the same as that of a rectangle of breadth12 cm. What is the length of the rectangle?​

Answer»

Answer :-

Given :-

  • The AREA of a square of side 18 cm is the same as that of a rectangle of breadth 12 cm.

To find :-

  • The length of the rectangle.

Step-by-step explanation :-

  • Before finding the length of the rectangle, let's find the area of the square FIRST!

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We KNOW that :-

\underline{\boxed{\sf Area \: of \: a \: square = Side \times Side.}}

Here,

  • Side = 18 cm.

Hence,

\boxed{\sf Area = 18 \times 18}

\overline{\boxed{\sf Area = 324 \: cm^2}}

  • Hence, the area of the square is 324 cm².

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  • Now, it has been given that the area of the square and the rectangle is same.

  • So, the area of the rectangle is 324 cm².

  • Therefore lets find the length of the rectangle now.

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We know that :-

\underline{\boxed{\sf Area \: of \: a \: rectangle = Length \times Breadth}}

Here,

  • Area = 324 cm².
  • Breadth = 12 cm.

  • Let the length be l.

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{\underline{\underline{\mathfrak{Substituting \: these \: values\: in\: the\: formula,}}}}

\boxed{\rm324 = l \times 12}

Multiplying l by 12,

\boxed{\rm324 = 12l}

Transposing 12 from RHS to LHS, changing it's sign,

\boxed{\rm\dfrac{324}{12} = l}

Dividing 324 by 12,

\overline{\boxed{\rm27 \: cm = l.}}

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  • Hence, the length of the rectangle is 27 cm.


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