The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq.cm. What is the length of the rectangle?
18 cm
16 cm
40 cm
20 cm
Explanation:
Let breadth = $x$ cm
Then length = 2$x$ cm
Area = lb = $x \times 2x$ = 2$x$2
New length = $\left(2x - 5\right)$
New breadth =$\left (x + 5\right)$
New Area = lb = $\left(2x - 5\right)\left(x + 5\right)$
But given that new area = initial area + 75 sq.cm.
=> $\left(2x - 5\right)\left(x + 5\right)$ = 2$x$2 + 75
=> 2$x$2 + 10$x$ - 5$x$ - 25 = 2$x$2 + 75
=> 5$x$ - 25 = 75
=> 5$x$ = 75 + 25 = 100
=> $x$ = $\dfrac{100}{5}$ = 20 cm
Length = 2$x$ = 2 × 20 = 40cm