Math, asked by Anonymous, 7 hours ago

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.

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Answers

Answered by Athul4152
8

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}

Answered by Aryan0123
12

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

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