Question

If the length and breadth of a rectangle be increased by 2 m and 3 m respectively, the area
of the rectangle is increased by 75 sq m. But if the length be decreased by 2 m and the
breadth be increased by 3 m, the area of the rectangle increases by 15 sq m. Find the
dimensions of the rectangle.
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Answer 1

Explanation:

Let length and breadth of a rectangle is x and y. Then, as per first condition,

(x-5)(y+3)=xy-9

=> xy-5y+3x-15=xy-9

=> 3x-5y=6 .....(i)

As per second condition,

(x+3)(y+2)=xy+67

=> xy+3y+2x+6=xy+67

=> 2x + 3y = 61 .....(ii)

On multiplying Eq. (i) by 3 and Eq. (ii) by 5 then adding, we get

9x - 15y = 18

10x + 15y = 305

----------------

=> 19x = 323

=> x = 32319=17

Hence, the length of rectangle is 17 m

$\red{hope \: this \: helps}$

Answer 2

Let the width of the rectangle = x units

Length = (2 x + 5) units

According to the question,

Area = x(2x + 5)

=> 75 = 2x2+5x

=> 2x2+5x−75=0

=> 2x2+15x−10x−75=0

=> x(2x+15)-5(2x+15)=0

=> (2x+15)(x-5)=0

=> x = 5 and −152

Width cannot be negative.

Width = 5 units

Length=2x+5 =2×5+5=15 units

Perimeter of the rectangle

= 2(15 + 5) = 40 units

Hope helps