Question

A rectangular field is 0.4 m longer than it is wide. If its length is 6m find its Perimeter.. When the breadth of the rectangle is reduced by 0.5m. the length is increased such that the perimeter is increased by 1/4 of its Original What is the Change in the length of the rectangle ?​

Answer 1

Let the width of the rectangular field be x. Then, the length would be x + 0.4 m.

The original perimeter of the rectangle would be:

P = 2 (x) + 2 (x + 0.4) = 4x + 0.8

We know that the perimeter increased by 1/4 of its original value, so:

P' = P + P/4 = 4x + 0.8 + (4x + 0.8)/4 = 4x + 0.8 + x + 0.2 = 5x + 1

So, the new perimeter is 5x + 1 m.

We also know that the width of the rectangle was reduced by 0.5 m, so the new width is x - 0.5 m. And the new length was increased, but we don't know by how much, so let's call that increase ΔL.

The new perimeter would be:

P' = 2 (x - 0.5) + 2 (x + ΔL + 0.4) = 4x + 2ΔL - 1

So, equating the two expressions for P' that we derived above:

5x + 1 = 4x + 2ΔL - 1

Solving for ΔL, we get:

ΔL = (5x + 2 - 4x)/2 = (x + 2)/2 = (6 + 2)/2 = 4 m

So, the change in the length of the rectangle is 4 m.