Question

9.The length of a rectangular plot exceeds its breadth by 5 m. If the perimeter of the plot is 142 m, find the
dimensions of the plot.
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Answer 1

Step-by-step explanation:

Let breadth be = x

Length = x+5m

2(x+x+5m) = 4x + 10

4x + 10m = 142 m

4x = 132 m

x = 33 m

Lengths are = 33m,38m

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Answer 2

Given:-

Perimeter of the rectangular plot = 142 m

To find:-

Dimensions of the rectangular plot

Assumption:-

Let the breadth be (x) m

Hence, Length = (x + 5) m

Solution:-

ATQ,

$\sf{Perimeter\:of\:the\:plot = 142}$

= $\sf{2(Length+ Breadth) = 142}$

$\sf{\implies 2[(x)+(x+5)] = 142}$

$\sf{\implies x+x+5 = \dfrac{142}{2}}$

$\sf{\implies 2x + 5 = 71}$

$\sf{\implies 2x = 71 - 5}$

$\sf{\implies 2x = 66}$

$\sf{\implies x = \dfrac{66}{2}}$

$\sf{\implies x = 33}$

Therefore,

$\sf{Length \:of \:the \:rectangular\: plot = (x + 5)m = (33 + 5)m = 38 m}$

$\sf{Breadth\:of\:the\:rectangular\:plot = (x)m = 33m}$

Some common formulas:-

• $\sf{Area\:of\:Square = (Side)^2\:sq.units}$

• $\sf{Perimeter\:of\:Square = 4(side)\:units}$

• $\sf{Area\:of\:Rectangle = (Length\times Breadth)\:sq.units}$

• $\sf{Perimeter\:of\:Rectangle = 2(Length + Breadth)\:units}$