Question

he length of a rectangle is twice that of its breadth. If the length of the rectangle is increased by 15% while its breadth is decreased by 12% determine, if any the percentage change in its perimete

Answer 1

Answer:

Step by step explanation of the problem:

Let L, B be length and breadth of rectangle,

then the area of rectangle is

A1 = L * B …..(1)

Here in the question it’s given that the length decreased by 15% and breadth increased by 20%.

So, new length(L1) = L – L * 15%

= L(1 – 15%)

= L(1 – 0.15)

= L(0.85).

New breadth(B1) = B + B * 20%

= B(1 + 20%)

= B(1.20).

New Area of rectangle(A2) = L * 0.85 * B * 1.20

= 1.02LB.

Change in area of rectangles = A2 – A1

= 1.02LB – LB

= 0.02LB

= 2% of A1. (from eq1)

Percentage change in area of rectangle = change in area / original area

= 2 % A1 / A1

= 2%.

Therefore, the percentage change on decreasing the length of a rectangle by 15% and increasing the breadth of a rectangle by 20% is 2%. Or we can say that the area of rectangle increases by 2% on decreasing the length by 15% and increasing the breadth by 20%.