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.

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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