Question

The width of a rectangle is two-thirds its length. if the perimeter is 90 meters, find the dimensions of the rectangle

Answer 1

SOLUTION :

The width (breadth) of a rectangle is two-thirds its length   (given)

The perimeter of the rectangle = 90 m

To be found :-

The dimensions of the rectangle

Let

The length of the rectangle be x m

So, the breadth = $\bf \frac{2x}{3}$ m

We know that,

Perimeter of rectangle = 2(l+b) units  

[ ∴  in which l is the length and b is the breadth of the rectangle ]

⇒ $\bf 90 =2( x + \frac{2x}{3})$

⇒ $\bf 90 = 2( \frac{3x+2x}{3})$

⇒ $\bf \frac{90}{2} = \frac{5x}{3}$

⇒ $\bf 45 \times 3 = 5x$

⇒ $\bf 135 = 5x$

⇒ $\bf \frac{135}{5}=x$

⇒ $\bf 27 = x$

Therefore

length of the rectangle (x) = 27 m

and the breadth of the rectangle ( $\bf \frac{2x}{3}$ ) = 18 m

Answer 2

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