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