Question

The length of a rectangle is 13 m longer than its breadth. If the perimeter of the
rectangle is 214 m, then find its area.
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Answer 1

$\sf \large \underbrace{ \underline{Understanding \: the \:Concept }}$

Here's the concept of perimeter as well as area of rectangle are used we have given the statement that length is 13m greater than the breadth and we have to find the area. To find the area of rectangle first we should know the values of its dimensions. So let's try to find the length and breadth first.

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Let breadth of rectangle be x

So length will be x+13.

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$\color{blue} \underline{ \boxed{ \sf★Perimeter \: of \: rectangle=2(L+B)}}$

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$\sf \small[Here \: L \: and \: B \: refers \: to \: Length \: and \: breadth \: of \: rectangle]$

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$\sf \implies \: 214m = 2(x + 13m + x)$

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$\sf \implies \: 214m = 2(13m + 2x)$

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$\sf \implies \: 214m = 26m+ 4x$

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$\sf \implies \: 214m - 26m = 4x$

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$\sf \implies \: 188m= 4x$

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$\sf \implies \: \dfrac{188m}{4}= x$

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$\large \color{skyblue} \boxed{\sf \implies \: 47m= x}$

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⊙ Breadth of rectangle=x=47m

⊙ Length of rectangle=x+13m=47m+13m

Length of rectangle=60m

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Now we have length and breadth of rectangle so we can easily find the area of rectangle.

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$\color{red} \underline{ \boxed{ \sf&#10029 \: Area \: of \: rectangle=Length×Breadth}}$

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$\sf \: Area \: of \: rectangle=47m \times 60m$

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$\sf \: Area \: of \: rectangle = {2820m }^{2}$

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Hence the area of rectangle is 2820m².

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$\sf \large \underbrace{ \underline{More \: formulae \: to \: know}}$

$\sf ★ \: Area \: of \: square=Side²$

$\sf★ \: Perimeter \: of \: square=4×Side$

$\sf★ \: Area \: of \: circle=πr²$

$\sf★ \: Perimeter \: of \: circle=2πr$

Answer 2

Answer:

1222

Step-by-step explanation:

length=13m

breadth=?

perimeter of rectangle=2(L+B)

214=2(13+B)

214=26+2B

214-26÷2=B

B=94

Area of rectangle=L×B

94×13=1222