if the ratio of the length to the breadth of a rectangle be 5:3 and its perimeter is 144m, find the length of the rectangle .

To find the length of the rectangle, given that the ratio of length to breadth is 5:3 and the perimeter is 144m, we can follow these steps:

Step 1: Let's assume the common ratio between the length and the breadth is k. Therefore, we can express the length as 5k and the breadth as 3k.

Step 2: The formula for the perimeter of a rectangle is P = 2(length + breadth). We are given that the perimeter is 144m, so we can write the equation as follows:

144 = 2(5k + 3k)

Step 3: Simplify the equation by distributing the 2 on the right side:

144 = 10k + 6k

Step 4: Combine like terms:

144 = 16k

Step 5: Divide both sides of the equation by 16 to isolate k:

k = 144/16

Step 6: Simplify:

k = 9

Step 7: Now that we have the value of k, we can find the length of the rectangle by substituting k back into the expression for the length:

length = 5k = 5(9) = 45

Therefore, the length of the rectangle is 45m.

perimeter: 2L+2B

144=2L+2B

but L/B=5/3 or L=5B/3

then 144=10B/3+2B=16B/3 or B= 3*144/16
solve for B, then L= 5B/3

18

Let the length be L. The width W must then be 3L/5, so that the L/W ratio is 5:3.

Also,

Perimeter = 2(L+W) = 144

2L + 2*(3L/5) = (16/5)L = 144
which leads to
L = 45 meters
W = (3/5)L = 27 meters