Question

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

QUESTION -

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

ANSWER -

Area of the rhombus = Side × Length of altitude to the corresponding side from opposite vertex

= 6 cm × 4 cm = 24 cm2

Let the length of the other diagonal is x.

It is known that the area of a rhombus is half of the product of diagonals of the rhombus.

∴ (1/2) × 8 cm × x = 24 cm2

⇒

x = (24 × 4) cm = 6 cm

Thus, the measure of the remaining diagonal of the rhombus is 6 cm.

Answer 2

Answer:-

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 ! If it plz follow and thanks my all answers.