Question

The area of a rectangle reduces by 160 m2 if its length is increased by 5m and breadth is reduced by 4m. However if length is decreased by 10m and breadth is increased by
2 m, then its area is decreased by 100m2. Find the dimensions of the rectangle.​

Answer 1

Answer:

Dimensions of the rectangle:

• Length = 60 m
• Breadth = 20 m

Step-by-step explanation:

Let length = l m, breadth = b m, Area = l × b m²

✏ Case I :

When l = l + 5, b = b - 4, Area = lb - 160

⇝ (l + 5)(b - 4) = lb - 160 (l × b = Area)

⇝ lb -4l + 5b -20 = lb - 160

⇝ -4l + 5b = -140

⇝ 4l - 5b = 140 → (1)

$\hrulefill$

✏ Case II :

When l = l - 10, b = b + 2, Area = lb - 100

⇝ (l - 10)(b + 2) = lb - 100 (l × b = Area)

⇝ lb - 2l - 10b -20 = lb - 100

⇝ 2l - 10b = -80 → (2)

Now, (2) × 2 ⇒

4l - 20b = -160 → (3)

Again, (3) - (1) ⇒

⇝ - 15b = - 300

⇝ b = 20 m

Substituting the value of b in (1) ⇒

⇝ 4l - 5 × 20 = 140

⇝ 4l = 240

⇝ l = 240/4 = 60 m

∴ length of rectangle = 60 m and breadth = 20 m.