the perimeter of a rectangle is 50m. the ratio of area and length is 5:1. find the value of length
Answers
Answer:
Step-by-step explanation:
FIND THE LENGTH
Given :-
Perimeter of rectangle = 50 m
Ratio of area and length = 5:1
Solution :-
Now, we know that the formula for calculating perimeter of a rectangle is 2(l + b) where l and b are length and breadth of the rectangle.
Let x = length of the rectangle.
2(x + b) = 50
x + b = 25
b = 25 - x
So now,
We have,
Length = x
Breadth = 25 - x
Now solving the ratio part of the question.
Area of a rectangle = l × b
5 : 1 = Area : Length
5 : 1 = x(25 - x) : x
5 = (x × (25 - x) / x
5 = (25x - x²)/x
5x = 25x - x²
x² - 25x + 5x = 0
x² - 20x = 0
x(x - 20) = 0
Now,
Either x = 0
or x - 20 = 0
Let us consider both the cases :-
When x = 0;
Length = x = 0m and
Breadth = 25 - x = 25 - 0 = 25m
When x - 20 = 0
x = 20
Length = x = 20m and
Breadth = 25 - x = 25 - 20 = 5m
Since, it is not possible to have a rectangle with 0m length, therefore, we will only consider the second case in which length = 20m.
Answer:
P=2(l+b)
50=2(l+b)
l+b=25
l=x b=25-x
x:area=1:5
x:(25-x)x=1:5
x:25x-xsquare=1:5
5x=25x-xsquare
5x+xsquare=25x
xsquare=20x
x=20x/x
x=20
length=20 breadth=25-20
=5