A rectangle has length & width in the ratio of 3:2.If the length is increased by 8 & width is increased by 50%.The ratio of new perimeter to original perimeter is 8:5.Find the area of new rectangle
let the length be 3x and
let the width be 2x
new length = 3x + 8
new width = 1.5(2x) = 3x
original perimeter = 2(3x) + 2(2x) = 10x
new perimeter = 2(3x+8)+ 2(3x)
= 12x + 16
(12x+16)/(10x) = 8/5
80x = 60x + 80
20x = 80
x = 40
so new length = 3(40)+8 = 128
new width = 3(40) = 120
new area = 128x120 = 15360
use the suitable units, you gave none.
"20x = 80
x = 40 "
How silly of me ! , that should have been
x = 4
so new rectangle is 20 by 12 for an area of 240
5yd 6yd u
To find the area of the new rectangle, we first need to determine the dimensions of the new rectangle. Let's go step by step.
Let the original length of the rectangle be 3x and the original width be 2x, where x is a common ratio.
The original perimeter is given by:
Original perimeter = 2(Length + Width) = 2(3x + 2x) = 2(5x) = 10x
Now, the length of the rectangle is increased by 8, so the new length becomes 3x + 8.
The width is increased by 50%, which means it becomes 2x + 0.5(2x) = 2x + x = 3x.
The new perimeter is given as 8:5 of the original perimeter:
New perimeter / Original perimeter = 8/5
Substituting the values of the perimeters:
(2(3x + 8) + 2(3x)) / (10x) = 8/5
Simplifying the equation:
(6x + 16 + 6x) / 10x = 8/5
(12x + 16) / 10x = 8/5
Cross-multiplying:
5(12x + 16) = 8(10x)
60x + 80 = 80x
Simplifying and solving for x:
20x = 80
x = 80/20
x = 4
Now that we know x = 4, we can find the dimensions of the new rectangle:
Length = 3(x) + 8 = 3(4) + 8 = 12 + 8 = 20
Width = 2(x) + 0.5(2x) = 2(4) + 0.5(8) = 8 + 4 = 12
Therefore, the dimensions of the new rectangle are length = 20 and width = 12.
To find the area of the new rectangle, we multiply the length and width:
Area = Length x Width = 20 x 12 = 240 square units.
So, the area of the new rectangle is 240 square units.