Question

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. Find the length of the rectangle.

Answer 1

hope...it helps u..

length =40cm

Answer 2

$Let \: breadth \: of \:a \: rectangle (b) = x \:cm$

$Length (l) = 2\times (breadth) = 2x \:cm$

/* According to the problem given */

if its length is decreased by 5 cm and breadth is increased by 5 cm */

$New \: breadth (B) = (x+5) \:cm \\New \: length (L) = (2x-5) \:cm$

$Now, Area _{(New) } - Area _{(Old)} = 75 \:cm^{2}$

$\implies L\times B - l \times b = 75$

$\implies (2x-5)(x+5) - (2x) \times x = 75$

$\implies 2x^{2} + 10x - 5x - 25 - 2x^{2} = 75$

$\implies 5x - 25 = 75$

$\implies 5x = 75 + 25$

$\implies 5x = 100$

$\implies x = \frac{100}{5}$

$\implies x = 20 \:cm$

$Now, Length \:of \:the \: rectangle (l) = 2x \\= 2 \times 20\:cm \\= 40 \:cm$

Therefore.,

$\red { Length \:of \:the \: rectangle} \green {= 40 \:cm}$

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