Question

the perimitre of a rectangle is 80 metre and its length is one metre more than twice the breadth what are its length and breadth​

Answer 1

• The length of the rectangle = 27 m.
• The breadth of the rectangle = 13 m.

Given :–

• The perimeter of a rectangle = 80 m.
• The length is one meter more than twice the breadth.

To Find :–

• The length and the breadth of a rectangle.

Solution :–

Let,

The breadth be x.

The length be 2x + 1 because in the given question, the length is one metre more than twice the breadth.

And given that,

Perimeter of the rectangle = 80m

2(l + b) = 80m

Now, substitute the value of the length and the breadth in the formula of perimeter of the rectangle.

$\implies2(2x + 1 + x) = 80 \: m$

$\implies 2x + 1 + x = \cancel\dfrac{80}{2} \: m$

$\implies 3x + 1 = 40 \: m$

$\implies 3x = 40 - 1 \: m$

$\implies 3x = 39 \: m$

$\implies x = \cancel\dfrac{39}{3} \: m$

$\implies x = 13 \: m$

So,

The breadth = x = 13 m.

The length = 2x + 1 = 2(13) + 1 = 26 + 1 = 27 m.

Hence,

The length and the breadth of the rectangle is 13m and 27m.

Verification :–

Given that,

Perimeter of the rectangle = 80m

2(l + b) = 80m

We have,

• l = 27.
• b = 13.

Now, substitute both the values in the formula of perimeter of the rectangle.

$\implies 2(27m+ 13m) = 80 \: m$

$\implies 2(40m) = 80 \: m$

$\implies 2 \times 40 \: m = 80 \: m$

$\implies 80 \: m = 80 \: m$

Hence Verified !