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Linear Equations in Two Variables — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsLinear Equations in Two Variables5 Marks
Question
If in a rectangle, the length is increased and breadth reduced each by 2 units, the area is reduced by 28 square units. If, however the length is reduced by 1 unit and the breadth increased by 2 units, the area increases by 33 square units. Find the area of the rectangle.
✓

Answer

Let the length and breadth of the rectangle be x and y units respectively.
Then area of rectangle = xy square units
It is given that if length is increared and breadth reduced each by 2 units. then the area is reduced by 28 square units.
⇒ (x + 2) (y - 2) = xy - 28
⇒ xy - 2x + 2y - 4 = xy - 28
⇒ -2x + 2y - 4 + 28 = 0
⇒ -2x + 2y + 24 = 0
⇒ 2x - 2y - 24 = 0 ......(i)
It is also given that the length is reduced by 1 unit and breath is increcred by 2 units then the area is increared by 33 square units.
⇒ (x - 1) (y + 2) = xy + 33
⇒ xy + 2x - y - 2 = xy + 33
⇒ xy + 2x - y - 2 - xy - 33 = 0
⇒ 2x - y - 35 = 0 ......(ii)
Now, subtracting eq. (ii) from eq. (i) and we get
⇒ 2x - 2y - 24 - (2x - y - 35) = 0
⇒ 2x - 2y - 24 - 2x + y + 35 = 0
⇒ -y + 11 = 0
⇒ y = 11
Putting the value of y in eq. (i)
⇒ 2x - 2y - 24 = 0
⇒ 2x - 2 × 11 - 24 = 0
⇒ 2x - 22 - 24 = 0
⇒ 2x - 46 = 0
⇒ x = 23
Hence, the length of the rectangle is 23 and breadth of the rectangle is 11
Area os rectangle = length × breadth
= 23 × 11
= 253 square units.

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