# Find the perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm

**Solution:**

For a better understanding of this question understand it with the help of a figure.

As it is mentioned in the question suppose there is a rectangle ABCD and whose length is given 40 cm.

As we know the opposite sides of a rectangle are equal if AB = 40 cm that means the side opposite to AB i.e. CD will also be 40 cm.

Now, one of the diagonals of a rectangle is given AC = 41cm it divides the rectangle into two right-angled triangles.

Now, you can apply the Pythagoras theorem and find the third side that is the breadth of the rectangle.

Now, you have the measure of both the sides of a rectangle i.e. length and breadth, you can easily find out the perimeter of the rectangle.

Given, in rectangle ABCD, AB and CD are the lengths of the rectangle. AB = 40 cm, CD = 40 cm and AC is the diagonal.

Therefore, AC = 41 cm

Let breadth of rectangle be x.

Now, in triangle ADC, by Pythagoras theorem (Hypotenuse)^{2} = (Perpendicular)^{2} + (Base)^{2}

(AC)^{2} = (DC)^{2} + (AD)^{2}

(41)^{2} = (40)^{2} + (x)^{2}

1681= 1600 +(x)^{2}

1681–1600 = (x)^{2}

x^{2} = 81

⇒ x = 9 cm

Therefore, breadth of rectangle = 9 cm

As we know that Perimeter of rectangle = 2(l + b)

= 2(40 + 9)

= 2(49)

= 98 cm

Hence, the perimeter of rectangle is 98 cm

Useful Tip: whenever you encounter problems of this kind, remember the Pythagoras property of the right-angled triangle and the formulas related to the rectangle.

**Video Solution:**

## Find the perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm

### NCERT Solutions for Class 7 Maths - Chapter 6 Exercise 6.5 Question 7

Find the perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm

The perimeter of the rectangle is 98 cm