The length of a rectangle is $15 c m$ and breadth is $8 c m .$ If the length is increased by $5 c m$ and breadth is increased by $2 c m,$ then the increase in area is equal to

$40 c m^{2}$

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$80 c m^{2}$

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$60 c m^{2}$

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$100 c m^{2}$

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Solution

The correct option is B: $80 c m^{2}$

Let $A B C D$ be the rectangle with $A B = 15 c m$ and $C B = 8 c m .$

Let the length and breadth be increased by $5 c m$ and $2 c m$ respectively as shown.

Area of original rectangle $A B C D = 15 \times 8 c m^{2}$

Area of new rectangle $A E G I$ will be

area $A B C D +$ area $D C F E +$ area $C H G F +$ area $B I H C$

$= (15 \times 8) + (2 \times 15) + (2 \times 5) + (8 \times 5)$

Hence, increase in area $=$ area of rectangle $A E G I -$ Area of rectangle $A B C D$
$= [$ area $A B C D +$ area $D C F E +$ area $C H G F +$ area $B I H C]$ - area $A B C D$
$=$ area $D C F E +$ area $C H G F +$ area $B I H C$

$= (2 \times 15) + (2 \times 5) + (8 \times 5)$

$= 30 + 10 + 40$

$= 80 c m^{2}$

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The length of a rectangle is 15 cm and breadth is 8 cm. If the length is increased by 5 cm and breadth is increased by 2 cm, then the increase in area is equal to

The length of a rectangle is $15 c m$ and breadth is $8 c m .$ If the length is increased by $5 c m$ and breadth is increased by $2 c m,$ then the increase in area is equal to