community around the world.

Activity Discussion Math Mensuration Reply To: Mensuration

• ### Akash

Member
June 22, 2023 at 4:01 pm
0

To solve this problem, let’s assume the original length of the rectangle is L and the original width is W. The original area of the rectangle is given by A = L * W.

According to the problem, the length is increased by 34%. This means the new length is L + 0.34L = 1.34L.

Now, we want to find the percentage reduction in the width, which we’ll represent as x%. The new width would then be (1 – x/100)W, since the width is reduced by x%.

To keep the area of the rectangle the same, the original area (A) should be equal to the new area (A’). So, we have:

A = A’

L * W = (1.34L) * ((1 – x/100)W)

To simplify the equation, we can cancel out the common factors:

1 * W = 1.34 * (1 – x/100) * W

Now, we can cancel out the width (W) from both sides:

1 = 1.34 * (1 – x/100)

Next, we can simplify the equation further:

1 = 1.34 – 1.34x/100

Now, let’s isolate the x term by moving the constants to the other side:

1.34x/100 = 1.34 – 1

Simplifying:

1.34x/100 = 0.34

Now, we can solve for x by cross-multiplying:

1.34x = 0.34 * 100

1.34x = 34

Dividing both sides by 1.34:

x = 34/1.34

x â‰ˆ 25.37

Therefore, the width should be reduced by approximately 25.37% to keep the area of the rectangle the same when the length is increased by 34%.

+