Question

the perimeter of a rectangle is 13 cm and its width is 11/4 cm . find its area

Answer 1

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Answer 2

${\underline{\underline{\red{\sf{Given:}}}}}$

• Perimeter of a rectangle is 13cm.
• Width of rectangle is 11/4cm.

${\underline{\underline{\red{\sf{To\:Find:}}}}}$

• Area of the rectangle.

${\underline{\underline{\red{\sf{Concept\:Used:}}}}}$

• We will use formula for find perimeter of a rectangle to obtain length.
• Using that we will find area.

${\underline{\underline{\red{\sf{Answer:}}}}}$

Let us take the length of the rectangle be x cm.

Now it's given breadth is 11/4cm and perimeter 13cm.

We know ,

$\large{\boxed{\red{\sf{Perimeter_{rectangle}=2(l+b)}}}}$

$\sf{\implies 2(l+b) =13cm}$

$\sf{\implies 2(x+\dfrac{11cm}{4})=13cm}$

$\sf{\implies 2x +\dfrac{11\:cm}{2}=13cm}$

$\sf{\implies \dfrac{4x+11}{2}=13cm}$

$\sf{\implies 4x+11=2\times 13cm}$

$\sf{\implies 4x+11=26cm}$

$\sf{\implies 4x=26-11}$

$\sf{\implies 4x=15}$

${\underline{\boxed{\red{\sf{\leadsto x=\dfrac{15\:cm}{4}}}}}}$

Therefore the length of the rectangle is 15/4cm.

Now ,Area of rectangle is given by ;

$\large{\boxed{\red{\sf{Area_{rectangle}=length\:\times breadth}}}}$

$\sf{\implies Area =\dfrac{11cm}{4}\times \dfrac{15cm}{4}}$

$\sf{\red{\leadsto Area =\dfrac{165cm^{2}}{16}}}$

Therefore area is 165cm²/16 =10.315cm² .