The length of a rectangul has increased in the ratio 3:2 and the width reduced in the ratio 4:5.If the original length and width were 18cm and 15cm respectively. Find the ratio of change in it's area
answer
work
L2 = 1.5 L
W2 = 0.8 W
L2*W2 = 1.5 * 0.8 L W = 1.2 * LW
1.2= 12/10 = 6/5
or just
3/2 * 4/5= 6/5
but that is too easy
To find the ratio of change in the area of the rectangle, we need to calculate the original area and the new area, and then determine the ratio between them.
1. Calculate the original area:
Original Area = Length * Width = 18 cm * 15 cm = 270 cm²
2. Calculate the new length and width:
New Length = Original Length * Ratio Increase = 18 cm * (3/2) = 27 cm
New Width = Original Width * Ratio Decrease = 15 cm * (4/5) = 12 cm
3. Calculate the new area:
New Area = New Length * New Width = 27 cm * 12 cm = 324 cm²
4. Calculate the ratio of change in the area:
Ratio of Change = New Area / Original Area = 324 cm² / 270 cm² = 1.2
Therefore, the ratio of change in the area of the rectangle is 1.2.