Question

the width of a rectangle is two thirds its length if the perimeter is 180 metre find the dimensions of the rectangle

( please Full Answer )

Answer 1

Let the length of the rectangle be 'l' and the breadth be 'b'. 

b = 2/3 l Perimeter

= 180 2(l + b)

= 180 2(l + 2/3 l)

= 180 2(5/3 l)

= 180 10/3 l

= 180 l

= 180 x 3/10 l

= 54 

Therefore length of the rectangle is 54 m and the breadth is 2/3 x 54 i.e. 36 m.


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OR
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Let

w = the width of the rectangle

l = the length of the rectangle

The width of a rectangle is two-third of its length

w = (2/3)l

The perimeter is 180 m

2(l + w) = 180 divide both sides by 2

l + w = 90

By solving the system of equations

w = (2/3)l

l + w = 90

We find....

l = 54 m

w = 36 m

Answer 2

HEY FRIEND ✌✌✌✌✌ HERE'S YOUR ANSWER
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Let the length of the rectangle - x
Let the breadth of the rectangle - y
given that ,
$y = \frac{2}{3} x$
and the perimeter =180
$2(x + y) = 180$
put the value of y in the formula :

$2(x + \frac{2}{3} x) = 180$
$2(x + \frac{2x}{3} ) = 180$
2(3x+2x/3)=180
2(5x/3)=180

$\frac{10x}{3} = 180$
$10x = 540$
$x = 54$
length=54
put the value of x in eq 1 i.e,
$y = \frac{2}{3} x$
$y = \frac{2}{3} \times 54$
y=36

therefore, length=54cm
breadth = 36cm

HOPE IT WORKS FOR U