Question

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

Answer 1

Answer:

• the perimeter of rectangle is 2×l+b = 2×40+41 = 2×81 = 162

Answer 2

Given :-

Length of the rectangle = 40 cm

Diagonal of the rectangle = 41 cm

To Find :-

The breadth of the rectangle.

The perimeter of the rectangle.

Analysis :-

Using the Pythagorean theorem, find the breadth of the rectangle.

Substitute the values in the formula of perimeter of rectangle and solve it.

Solution :-

We know that,

• l = Length
• b = Breadth
• p = Perimeter

According to the question,

The diagonal of the rectangle divides it into two right-angled triangles.

By the Pythagorean theorem,

$\underline{\boxed{\sf Hypotenuse=Length^{2}+Breadth^{2}}}$

Given that,

Length of the rectangle = 40 cm

Diagonal of the rectangle = 41 cm

Substituting their values,

$\sf 41^{2}=40^{2}+Breadth^{2}$

$\sf 1681 = 1600 + Breadth^{2}$

By transposing,

$\sf 1681 - 1600=Breadth^{2}$

$\sf Breadth^{2} = 81$

$\sf Breadth = \sqrt{81}$

Breadth = 9 cm

By the formula,

$\underline{\boxed{\sf Perimeter \ of \ rectangle=2(Length+Breadth)}}$

We know that,

Length = 40 cm

Breadth = 9 cm

Substituting their values,

Perimeter = 2 (40 + 9)

Perimeter = 2 (49)

Perimeter = 98 cm

Therefore, the perimeter of the rectangle is 98cm.