Question

A wire is 72 cm long. It is bent to form a rectangle: the ratio of its length to its breadth is 7: 5. Find the area of the rectangle.

Answer 1

Hint:Here a wire is bent to form a rectangle so the perimeter of thus formed rectangle will equal to the length of wire. The ratio of its length and breadth is also given so we can find its length and breadth from the given information then we find the area of the rectangle.

Complete step-by-step answer:
Let the ‘l’ and ‘b’ be the length and breadth of the rectangle respectively.
The ratio of its length and breadth is also given i.e 7: 5
Therefore, $l = 7x$ and $b = 5x$ .
As we know that perimeter P of the rectangle is given by
$P = 2\left( {l + b} \right)$ where ‘l’ and ‘b’ be the length and breadth of the rectangle respectively.
Since the rectangle is formed by bending of wire, so the perimeter of the rectangle will be equal to the length of wire.
Therefore, 2(l + b) = 72
$ \Rightarrow $ 2(7x + 5x) = 72
$ \Rightarrow $ 14x+10x = 72
$ \Rightarrow $ 24x = 72
$ \Rightarrow $ x = 3
Thus we get l = 7x = 7 x 3 = 21 cm
And b = 5x = 5 x 3 = 15 cm
Now, we know that area A of the rectangle is given by
A = lb = 21 x 15 $c{m^2}$ = 315 $c{m^2}$
Thus the required area of the rectangle is 315 $c{m^2}$

Note:In these types of questions, the perimeter remains the same as the same wire is bent into a rectangle.Rectangle is the quadrilateral in which each pair of opposite sides is equal and each angle is right angle i.e. 90 degree. The perimeter of the rectangle is = 2(l + b). The area of the triangle = l x b where l and b are the length and breadth of the rectangle. Students should know these formulas for solving these types of questions.