# 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 let's understand it with the help of a figure as shown below.

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 = 41 cm which divides the rectangle into two right-angled triangles.

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

Let the breadth of the rectangle be AD = 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 the rectangle = 9 cm

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

= 2(40 + 9)

= 2(49)

= 98 cm

Hence, the perimeter of the rectangle is 98 cm.

**ā Check: **NCERT Solutions for Class 7 Maths Chapter 6

**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

**Summary:**

The perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm is 98 cm.

**ā Related Questions:**

- Pqr Is A Triangle Right Angled At P If Pq 10 Cm And Pr 24 Cm Find Qr
- Abc Is A Triangle Right Angled At C If Ab 25 Cm And Ac 7 Cm Find Bc
- A 15 M Long Ladder Reached A Window 12 M High From The Ground On Placing It Against A Wall At A Distance A Find The Distance Of The Foot Of The Ladder From The Wall
- Which Of The Following Can Be The Sides Of A Right Triangle I 25 Cm 65 Cm 6 Cm Ii 2 Cm 2 Cm 5 Cm Iii 15 Cm 2cm 25 Cm

visual curriculum