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If the area of a rectangle is 84 sqcm and the difference of its length and breadth is 5cm,find its length,breadth and perimeter?

The eighth qstn in the two sums I have doubt pls help

1 Answer

Dec 25, 2016

Length, Breath $= 12, 7$ $= 12, 7$ (cm)
Perimeter $= 38$ $= 38$ (cm)

Explanation:

If the longer side is called the length and the length is called $L$ $L$ ; call the breadth $B$ $B$ .

Then we are told:
[1] $XXX B = L + 5$ $color(white)("XXX")B=L+5$ (cm)
and
[2] $XXX B \cdot L = 84$ $color(white)("XXX")B * L = 84$ (sq.cm.)

Substituting $(L + 5)$ $(L+5)$ from [1] for $B$ $B$ in [2]
[3] $XXX (L + 5) \cdot L = 84$ $color(white)("XXX")(L+5) * L =84$

[4] $XXX L^{2} + 5 L = 84$ $color(white)("XXX")L^2+5L =84$

[5] $XXX L^{2} + 5 L - 84 = 0$ $color(white)("XXX")L^2+5L-84=0$

[6] $XXX (L + 12) (L - 7) = 0$ $color(white)("XXX")(L+12)(L-7)=0$

[7] $color(white)("XXX"){:(L=-12,color(white)("X")orcolor(white)("X"),L=7), ("impossible",,):}$

Since $B=L+5$
$color(white)("XXX")B=12$

$"Perimeter " = 2xx ("Length" + "Breadth")=2xx(7+12)=38$

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