Question

Find the semiperimeter of a rhombus, the length of whose diagonals are 10 cm and 24 cm.​

Answer 1

Diagonals meet at the centre and forms right-angled triangles. Hence the side of the rhombus is 13cm.

Answer 2

Given :-

Diagonals of rhombus = 10cm and 24cm

To find :-

Semi perimeter of the rhombus

Rhombus properties :-

• Diagonals bisect each other (divide them into 2 equal parts)
• Diagonals bisect at 90°
• All sides are equal
• Opposite angles are equal
• Adjacent angles add up to 180° (supplementary)

As we know that the diagonals bisect each other at 90° to find the side of the figure, Pythagoras theorem should be used

Pythagoras theorem :-

The Pythagoras theorem states that, in any right angled triangle, the height squared added to the base squared will be equal to the hypotenuse squared (hypotenuse is the longest side of the triangle)

Let us take ∆DOC.

In this triangle,

OC = base

DO = height

DC = Hypotenuse

DO = 12cm (as diagonals bisect each other)

OC = 5cm (diagonals bisect each other)

By using the theorem

(OC)² + (DO)² = (DC)²

(5)² + (12)² = (DC)²

25 + 144 = (DC)²

169 = (DC)²

By transposing the power,

√169 = (DC)

13cm = DC

SEMI PERIMETER :-

Now that we know the side of the figure, let's find the semi perimeter.

WHAT IS PERIMETER ?

Perimeter refers to the total measurement of the boundry of a figure.

Perimeter of rhombus = side + side + side + side = 4 × side

Semi perimeter is half of the perimeter

Hence,

Perimeter of rhombus = 4 × 13

Perimeter = 52cm

$semiperimeter = \dfrac{52}{2}$

Semi perimeter = 26cm

EXTRAS :-

Perimeter of square = 4 × side

Perimeter of rectangle = 2(length+breadth)

Perimeter of traingle = Sum of it's sides