Question

If the length and breadth of a rectangle are in the ratio 4:3 and the area of the rectangle is 1728 sq .units, then find the length and breadth of the rectangle.

• A. length = 45 units and length = 16 units
• B. length = 48 units and breadth = 36 units
• C. length = 58 units and length = 26 units
• D. length = 144 units and length = 12 units

Answer 1

The correct option is B length = 48 units and breadth = 36 units

Given that length and breadth of the rectangle is in the ratio 4 : 3.

Let the length be 4$x$ and Breadth be 3$x$

Given area = 1728 sq.units

Area of a rectangle
$=\text{length}\times \text{breadth}=4x\times 3x$
$\Rightarrow$ 1728 = 12 $x^2$
$\Rightarrow$ $x^2$ = 144
$\Rightarrow$ $x$ = 12 units

Hence,
Length = 4$x$ = 4$\times$12 = 48 units
Breadth = 3$x$ = 3 $\times$ 12 = 36 units