Question

6. The length of a rectangle exceeds its breadth by 3 cm. Find the length and breadth of the rectangle if there perimeter is 26 cm.​

Answer 1

Step-by-step explanation:

Given :-

The length of a rectangle exceeds its breadth by 3 cm and there perimeter is 26 cm.

To find :-

Find the length and breadth of the rectangle ?

Solution :-

Let the breadth of a rectangle be X cm

Then , The length of the rectangle

= exceeds its breadth by 3 cm

= breadth + 3 cm

= X cm + 3 cm

Length of the rectangle = (X+3) cm

We know that

Perimeter of a rectangle = 2(l+b) units

We have , l = ( X+3 ) cm and b = X cm

On substituting these values in the above formula then

=> P = 2(X+3+X) cm

=> P = 2(2X+3) cm

=> P = (2×2X)+(2×3) cm

=> P = (4X+6) cm

According to the given problem

Perimeter of the rectangle = 26 cm.

=> 4X+6 = 26

=> 4X = 26 - 6

=> 4X = 20

=> X = 20/4

=> X = 5 cm

Now,

If X = 5 cm then X+3 = 5+3 = 8 cm

Therefore, length = 8 cm , breadth = 5 cm

Answer:-

The length and breadth of the given rectangle are 8 cm and 5 cm respectively.

Check :-

l = 8 cm , b = 5 cm

=> l = 5+3 cm

Length exceeds by 3 it's breadth

and

Perimeter = 2(l+b)

=> P = 2(8+5)

=> P = 2(13)

=> P = 26 cm

Verified the given relations in the given problem.

Used formulae:-

Perimeter of a rectangle = 2(l+b) units

Where, l and b are length and breadth of a rectangle respectively.