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Standard VI

Mathematics

Area of Square

A rectangle i...

Question

A rectangle is $8$ cm long and $5$ cm wide. Its perimeter is doubled when each of its sides is increased by x cm. Find the new length of the rectangle.

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Solution

$\to$ Original perimeter of
rectangle $= 2 (l + b) = 2 (8 + 5)$
$= 26 c m$
New perimeter $= 2 (l + x + b + x) = 2 \times 26$
$\Rightarrow l + b + 2 x = 32$
$\Rightarrow 13 + 2 x = 32$
$\Rightarrow 2 x = 19$
$\Rightarrow x = 9.5 c m$
$\Rightarrow$ New length $l + x = 8 + 9.5$
$= 17.5 c m$

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The length of a rectangle is 5cm less than twice its width. If the length is decreased by 5cm and its width is increased by 2cm, the perimeter of the resulting rectangle will be 74 cm. Find the length of the original rectangle.

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A rectangle is 8 cm long and 5 cm wide. Its perimeter is doubled when each of its sides is increased by x cm. Find the new length of the rectangle.

→ Original perimeter of rectangle =2(l+b)=2(8+5)=26cmNew perimeter =2(l+x+b+x)=2×26⇒l+b+2x=32⇒13+2x=32⇒2x=19⇒x=9.5cm⇒ New length l+x=8+9.5=17.5cm

A rectangle is $8$ cm long and $5$ cm wide. Its perimeter is doubled when each of its sides is increased by x cm. Find the new length of the rectangle.

$\to$ Original perimeter of
rectangle $= 2 (l + b) = 2 (8 + 5)$
$= 26 c m$
New perimeter $= 2 (l + x + b + x) = 2 \times 26$
$\Rightarrow l + b + 2 x = 32$
$\Rightarrow 13 + 2 x = 32$
$\Rightarrow 2 x = 19$
$\Rightarrow x = 9.5 c m$
$\Rightarrow$ New length $l + x = 8 + 9.5$
$= 17.5 c m$