Question

THE LENGTH AND DIAGONAL OF A RECTANGLE ARE 40 CM AND 41 CM.FIND ITS BREATH AND PERIMETER.

Answer 1

Given :-

The 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 :-

Consider the breadth as a variable.

Substitute the given values in the Pythagoras theorem.

After you get the value of the breadth, substitute the length and the breadth we got in the formula of perimeter of rectangle.

Solve it and you'll get the perimeter.

Solution :-

We know that,

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

Using the Pythagoras theorem,

$\underline{\boxed{\sf a^{2}+b^{2}=c^{2}}}$

Let the breadth be 'b' cm.

Given that,

Length (l) = 40 cm

Diagonal = 41 cm

Substituting their values,

$\sf (40)^{2}+(b)^{2}=(41)^{2}$

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

Transposing 1600,

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

$\sf b^{2}=81$

Finding the value of x,

$\sf b=\sqrt{81}$

$\sf b=9$

Therefore, the breadth is 9 cm.

By the formula,

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

Given that,

Length (l) = 40 cm

Breadth (b) = 9 cm

Substituting their values,

Perimeter = 2(40 + 9)

= 2(49)

= 98 cm

Therefore, the perimeter is 98 cm.