Question

The length of a rectangle is 3 times its breadth . If perimeter of the rectangle is 32 m find area.

Answer 1

Beginning the solution of such questions with assumption of variable is the best method to solve such problems.

Hence,
Let the breadth of rectangle be 'x'.
According to the question,
Length of rectangle = 3x

Now, we know that, the perimeter of a rectangle is equal to two times the sum of its length and it's breadth.
Perimeter of the rectangle = 2 ( l + b )
32 m = 2 ( 3x + x )
32 / 2 = 4x
4x = 16
x = 16 / 4
x = 4

Breadth of the rectangle = x = 4 m
Length of the rectangle = 3x = 3 * 4 = 12 m

Area of the rectangle = l * b = 4 * 12 = 48 m² or 48 sq. m

Answer 2

$let \: b = x \\ l = 3x \\ p = 32 \\ p = 2(l + b) \\ 32 = 2(3x + x) \\ \frac{32}{2} = 4x \\ \frac{16}{4} = x \\ x = 4 \\ b = 4 \\ l = 12 \\ area = l \times b \\ = 12 \times 4 \\ = 48 {m}^{2}$

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