Question

Find the area of a rhombus whose side is 5 cm and whose altitude is 4.8 cm. If one of its diagonals is 8 cm long, find the length of the other diagonal.

Note:
- Need full Explanation
- Dont Spam​

Answer 1

1. Area = 24 cm²

2. diagonal = 6 cm

$\bf\huge\underline{\underline{ Given :- }}$

• A rhombus is given

• its side is 5 cm

• altitude is 4.8 cm

• one of diagonal is 8 cm

$\bf\huge\underline{\underline{ To \: Find:- }}$

• area of the rhombus

• Length of other diagonal

$\bf\huge\underline{\underline{ Answer :- }}$

• Area of rhombus = b × h

• $\red{\implies}$ Area = 5 × 4.8

• $\red{\implies}$ Area = 24 cm²

$\rule{10cm}{0.05cm}$

• Another formula for rhombus = $\frac{1}{2}pq$
• where p and q are diagonals

• $\red{\implies}$ 24 = $\frac{1}{2}× 8 × q$

• $\red{\implies}$ 24 = 4q

• $\red{\implies}$ q = 6 cm

$\rule{10cm}{0.05cm}$

Answer 2

Answer :-

The length of other diagonal = 6 cm

Step-by-step explanation :-

Given:

• Side of rhombus = 5 cm
• Altitude (Height) of rhombus = 4.8 cm
• One of its diagonals = 8 cm

To find:

Length of other diagonal = ?

Solution:

A rhombus can be divided into 2 triangles.

Area of 1 triangle = ½ × Base × Height

Similarly,

Area of 2 triangles = 2 × ½ × Base × Height

→ Area of rhombus = Base × Height

We know that in a rhombus, all sides are equal.

So all sides can be considered as base

Substitute the given values of base and height in the above equation.

Area of rhombus = Base × Height

→ Area of rhombus = 5 × 4.8

→ Area of rhombus = 24 cm²

This area of rhombus can also be written as:

Area of rhombus = ½ × (Product of diagonals)

⇒ 24 = ½ × (d₁ × d₂)

⇒ 24 = ½ × (8 × d₂)

⇒ 24 = 4 × d₂

⇒ d₂ = 24 ÷ 4

⇒ d₂ = 6 cm

∴ The length of second diagonal = 6 cm