Ex.11.2 Q6 Mensuration Solution - NCERT Maths Class 8

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Question

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

 Video Solution
Mensuration
Ex 11.2 | Question 6

Text Solution

What is Known?

One of the diagonal, side and attitude of the rhombus.

What is unknown?

Area of the rhombus and length of the diagonal.

Reasoning:

Rhombus is a special case of parallelogram and the area of parallelogram is product of its base and height.

Steps:

Let the length of the other diagonal of rhombus is \(x.\)

Area of the rhombus \(ABCD\)

\[\begin{align} &= {\text{Base}} \times {\text{Length}}\\& = 5\,{\rm{cm}} \times 4.8 \, \rm{cm}\\ &= 24.0\,{{\rm{cm}}^2}\end{align}\]

Also,

Area of rhombus \(=\frac{1}{2}\times\) Product of its diagonals 

\[\begin{align} 24\,\text{cm}^{2} &=\frac{1}{2}(AD\times CB) \\  24\,\text{cm}^{2}&=\frac{1}{2}(x\times 8\,\text{cm}) \\ x\times 4\,\text{cm}&=24\,\text{c}{{\text{m}}^{2}} \\ x&=6\,\text{cm}\end{align}\]

Thus, area of the rhombus is \(24.0\,{{\rm{m}}^2}\) and length of the diagonals is \(6\,{\rm{cm}}\) .

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