Question

The length of a rectangle is twice its breadth. If its length is increased by 11 cm and breadth is decreased by 5 cm, the area of the rectangle is increased by 75 sq.cm. What is the length of the rectangle?

• A. 24 cm
• B. 261 cm
• C. 260cm
• D. 240 cm

Answer 1

Answer:

C. 260cm

Let’s solve step by step:

$\text{Let breadth} = x \text{ cm}$

$\text{Then length} = 2x \text{ cm}$

Original area:
$= 2x \cdot x = 2x^2$

New dimensions:
$\text{Length} = 2x + 11,; \text{Breadth} = x - 5$

New area:
$= (2x + 11)(x - 5)$

Given increase in area = 75:

$(2x + 11)(x - 5) = 2x^2 + 75$

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Expand:

$2x^2 - 10x + 11x - 55 = 2x^2 + 75$

$2x^2 + x - 55 = 2x^2 + 75$

Cancel $2x^2$:

$x - 55 = 75$

$x = 130$

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$\text{Length} = 2x = 260 \text{ cm}$

t{ cm}$