4. the area of a rectangle is 450 m^2. both the length and width of the rectangle are increased by 10%. what is the area of the new rectangle?
100% = 100 / 100 = 1
10 % = 10 / 100 = 0.1
100% + 10 % = 1 + 0.1 = 1.1
A = Original Area
A1 = New Area
Original Area:
A = W * L = 450 m ^ 2
New Area:
A1 = 1.1 * W * 1.1 * L
A1 = 1.1 * 1.1 * W * L
( Remark: W * L = A )
A1 = 1.21 * A
A1 = 1.21 * 450 = 544.5 m ^ 2
To find the area of the new rectangle, we need to first calculate the new length and width after they have been increased by 10%.
Let's assume the original length of the rectangle is L and the original width is W. We are given that the area of the rectangle is 450 m^2, so we can write the equation:
Area = Length x Width
450 = L x W
Now, we increase both the length and width by 10%. An increase of 10% can be calculated by multiplying the original value by 1.1 (which is equivalent to adding 10%).
New Length = L x 1.1
New Width = W x 1.1
Next, we find the area of the new rectangle by multiplying the new length by the new width:
New Area = New Length x New Width
New Area = (L x 1.1) x (W x 1.1)
New Area = 1.21 x L x W
So, the area of the new rectangle is 1.21 times the area of the original rectangle.
Substituting the known value of 450 m^2 for the original area, we can now calculate the area of the new rectangle:
New Area = 1.21 x 450
New Area = 544.5 m^2
Therefore, the area of the new rectangle is 544.5 m^2.