The length of the rectangle is 1.5 times its width. The length was reduced by 40% and the width was increased

| July 17, 2021 | education

The length of the rectangle is 1.5 times its width. The length was reduced by 40% and the width was increased by 40%. Decrease or increase its perimeter and by how many%?

If you designate the width of the figure as x, then the length, which is one and a half times larger, will be 1.5x.

After changing the parameters, the length of the new figure will be 1.5x – 40/100 * 1.5x. Let’s transform the expression:

1.5x – 0.4 * 1.5x = 1.5x – 0.6x = 0.9x.

The width of the new shape will be: x + 40 / 100x = x + 0.4x = 1.4x.

Let’s find what the perimeter of the original rectangle is:

2 * (x + 1.5x) = 2 * 2.5x = 5x.

Let’s find what the perimeter of the resulting figure is:

2 * (0.9x + 1.4x) = 2 * 2.3x = 4.6x.

This means the new perimeter will be smaller. Let’s find the percentage:

100 – 4.6x / 5x * 100 = 8 (%).

Answer: the perimeter of the resulting shape is smaller by 8%.



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