The area of a rectangle gets reduced by 9 square units if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and breadth by 2 units, the area is increased by 67 square units. Can you determine the length and breadth of the rectangle?

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Solution

Let length be l & breadth be b

Area of rectangle is =length×breadth

According to given condition,

(l−5)(b+3)=lb−9

⇒lb−5b+3l−15=lb–9

⇒3l−5b=6……(i)

Also,

(l+3)(b+2)=lb+67

2l+3b=61……(ii)

Solving (i) and (ii) we get,

2×(i)−3×(ii)⇒

6l−10b−6l−9b=12−183

−19b=−171⇒b=9

Substituting value of b in (i)

3l−5(9)=6⇒l=17

⇒l=17,b=9

∴ The length is 17 units and breadth is 9 units.

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State true or false:

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The area of a rectangle gets reduced by 9 square units. if its length is reduced by 5 units and breadth is increased by 3 units. However, if the length of this rectangle increases by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.

Let the length of the rectangle = x units and its breadth = y units

According to first condition :
$(x - 5) (y + 3) = x y - 9$ and

According to second condition:
$(x + 3) (y + 2) = x y + 67$

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