Question : The ratio of the length to the width of a rectangle is 3 : 2. If the length of this rectangle is increased by 25% and its width is kept constant, then the area of the rectangle increases by 24 m2. What is the width of this rectangle?
Option 1: 12 m
Option 2: 10 m
Option 3: 8 m
Option 4: 15 m
Correct Answer: 8 m
Solution :
Given,
The ratio of the length to the width of a rectangle is 3 : 2. If the length of this rectangle is increased by 25% and its width is kept constant, then the area of the rectangle increases by 24 m
2
.
We know,
Area of rectangle = length × width
Let the width of the rectangle be $x$.
⇒ The length is $\frac{3x}{2}$ and the area of the rectangle is $\frac{3x^2}{2}$
Now, the length is increased by 25%,
So, the new length is $\frac{3x}{2}×(1+\frac{25}{100})=\frac{3x}{2}\times(1.25)=\frac{15x}{8}$
And the area is $\frac{15x^2}{8}$
According to the question,
$\frac{15x^2}{8}=\frac{3x^2}{2}+24$
⇒ $(\frac{15−12}{8})x^2=24$
⇒ $x^2=\frac{24×8}{3}$
⇒ $x^2=64$
⇒ $x=\sqrt{64}$
⇒ $x=8$ m
Hence, the correct answer is 8 m.
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