Question

1. Find the area of a rhombus whose side is 6 cm and whose altitude is 4 cm. If one of its
diagonals is 8 cm long, find the length of the other diagonal.​

Answer 1

ANSWER:-

GIVEN:-

• Side = 6 cm.
• Altitude = 4 cm.
• Diagonal A = 8 cm.
• Length of Diagonal B = ?

Area of the rhombus = 6 cm × 4 cm = $24 {cm}^{2}$

Let the length of the other diagonal be B.

We know that,

Area of a rhombus = Half of the product of diagonals of the rhombus.

⇒ (1/2) × 8 cm × B = $24 {cm}^{2}$

⇒B = (24 × 4) cm = 6 cm.

Therefore, length of the other diagonal B = 6 cm.

WHAT IS A RHOMBUS?

◇ Rhombus is a quadrilateral as well as a parallelogram.

◇ Rhombus is also known as Rhomb.

◇ All sides are equal in length.

◇ Diagonals bisect each other at right angle.

◇ The opposite sides are parallel.

◇ Opposite angles are equal.

◇ It is often called a diamond.

◇ It is also referred to as convex quadrilateral.

Answer 2

$\large\red{\underline{\boxed{\textbf{ Thanks\:For\:Ansking}}}}$

Area of rhombus = 24 cm²

Length of the other diagonal = 6 cm.

Hi,

Given the side of the rhombus, b = 6 cm

Also, Given the altitude of rhombus , h = 4 cm,

Area of the rhombus when base(side) and altitude(h)

are given is given by A = base * height

Thus, Area of rhombus = 6 * 4  cm²

Area of rhombus = 24 cm².

Given one of the diagonal is of length  8 cm,

Let d₁ = 8 cm.

Let the length of the other diagonal be d₂.

If d₁, d₂ length of the diagonals are known, then

Area of rhombus is given by A = 1/2*d₁*d₂,

But we know, A = 24

Hence, 1/2*d₁*d₂ = 24

1/2*8*d₂ = 24

d₂ = 6 cm.

Hence, length of the other diagonal of rhombus

is 6 cm.

Hope, it helps !