A rectangle measures 20 cm by 15.If each dimension is increased by 2.5cm,by what percentage is:a)the perimeter of the rectangle increased b)the area of the rectangle is increased.Explain in detail
old p = 2(15+20) = 70
new p = 2(15+2.5 + 20+2.5) = 80
So, (a) 80/70 = 1.14
old a = 29*15 = 300
new a = (20+2.5)(15+2.5) = 393.75
So, (b) 393.75/300 = 1.31
now just express those factors as % increases
Explain further
Draw three rectangles with different measures having a perimeter of 20 cm:
To calculate the percentage increase in the perimeter and area of a rectangle, we need to follow these steps:
a) The perimeter of a rectangle is found by adding the lengths of all its sides. In this case, the original rectangle measures 20 cm by 15 cm, so its perimeter is (20 + 15 + 20 + 15) = 70 cm.
To find the new perimeter after increasing both dimensions by 2.5 cm, we add 2.5 cm to each side of the original rectangle. So the new dimensions would be (20 + 2.5) = 22.5 cm and (15 + 2.5) = 17.5 cm.
The new perimeter is then calculated using the same formula: (22.5 + 17.5 + 22.5 + 17.5) = 80 cm.
To find the percentage increase in the perimeter, we subtract the original perimeter from the new perimeter, divide the result by the original perimeter, and multiply it by 100.
Percentage increase in perimeter = ((80 - 70) / 70) * 100 = (10 / 70) * 100 ≈ 14.29%.
Therefore, the perimeter of the rectangle increases by approximately 14.29%.
b) The area of a rectangle is found by multiplying its length by its width. In this case, the original rectangle has an area of (20 * 15) = 300 cm^2.
To find the new area after increasing both dimensions by 2.5 cm, we add 2.5 cm to each side of the original rectangle. So the new dimensions would be (20 + 2.5) = 22.5 cm and (15 + 2.5) = 17.5 cm.
The new area is then calculated using the same formula: (22.5 * 17.5) = 393.75 cm^2.
To find the percentage increase in the area, we subtract the original area from the new area, divide the result by the original area, and multiply it by 100.
Percentage increase in area = ((393.75 - 300) / 300) * 100 = (93.75 / 300) * 100 ≈ 31.25%.
Therefore, the area of the rectangle increases by approximately 31.25%.