Question

aer
28. The ratio of length and breadth of a rectangle is 3:2 respectively.
The respective ratio of its peritaeter and area is 5:9. What is the
breadth of the rectangle in metre?
6 m
b. 8 m
c. 9 m
13 m
e. None
if he an
perim
a
20
Thor​

Answer 1

FINAL ANSWER:-

$breadth=6m$

GIVEN:-

ratio of length and breadth of a rectangle is 3:2

[∵ $length=3x$   ;    $breadth=2x$]

ratio of its perimeter and area is 5:9

[∵ $perimeter=5x$     ;     $area=9x$]

TO FIND:-

the  breadth of the rectangle in meter

FORMULAS USED:-

$perimeter\:of\:rectangle=2(l+b)$

$area\:of\;rectangle=l$×$b$

SOLUTION:-

$perimeter\:of\:rectangle=2(l+b)$

↔$putting\:values\:in\:equation$↔

we get.

$5x=2(3x+2x)\\5x=2(5x)\\5x=10x$← perimeter

⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔

$area\:of\;rectangle=l$×$b$

↔$putting\:values\:in\:equation$↔

we get.

$9x=3x*2x\\9x=6x^{2}$←area

Now,

according to question :-

$\frac{perimeter}{area}=\frac{5x}{9x}$

$\frac{5x}{9x} =\frac{10x}{6x^{2}}$

$10x*90x=6x^{2}*5x$  [∵by cross multiplication]

$90x^{2}=30x^{3}$

by factorisation of 90x²-30x³=0

$-30x^{2}(x-3)$

$x-3=0$ ⇒ $x=3$

∴$length=3x$ ⇒ $l=3*3$ ⇒ $length =9\:m$

∴$breadth=2x$ ⇒ $b=2*3$ ⇒ $breadth=6m$

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