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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.

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

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

x2 = 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.

☛ 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.

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