Question

perimeter of rectangle is 50m, the ratio of area and length is 5:1, find its length?​

Answer 1

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Answer 2

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.