The perimeter of a rectangle is 46 m and its length is 15 m. Find its :

(i) breadth

(ii) area

(iii) diagonal

(i) Given:

The perimeter of the rectangle is 46 m.

The length of the rectangle is 15 m.

Let the breadth of the rectangle be b m.

As we know, the perimeter of the rectangle = 2(length + breadth)

⇒ 2(15 + b) = 46

⇒ 15 + b = $\dfrac{46}{2}$

⇒ 15 + b = 23

⇒ b = 23 - 15

⇒ b = 8 m

Hence, the breadth of the rectangle is 8 m.

(ii) The area of the rectangle = length x breadth

= 15 x 8 m²

= 120 m²

Hence, the area of the rectangle is 120 m².

(iii) By using Pythagoras theorem,

⇒ Diagonal² = Length² + Breadth²

⇒ Diagonal² = 15² + 8²

⇒ Diagonal² = 225 + 64

⇒ Diagonal² = 289

⇒ Diagonal = $\sqrt{289}$

⇒ Diagonal = 17 m

Hence, the diagonal of the rectangle is 17 m.