Ex.3.3 Q8 Understanding Quadrilaterals Solution-Ncert Maths Class 8

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Question

The following figures \(GUNS\) and \(RUNS\) are parallelograms. Find \(x\) and \(y\). (Lengths are in \(\rm cm\))

Text Solution

i) What is Known?

Given figure is a parallelogram.

What is Unknown?

Values of \(x\), \(y\)

Reasoning:

The diagonals of a parallelogram bisect each other, in a parallelogram, the opposite sides have same length.

Steps:

In a parallelogram, the opposite sides have same length.

\[\begin{align}{\rm{SG}}\,\rm&= \,{\rm{NU}}\\3x &= 18\\x &= \,\frac{{18}}{3}\\x &= 6\end{align}\]

And,

\[\begin{align}\text{SN}&=\text{GU} \\ 26&=3y-1  \\ 3y&=26+1  \\y&=\frac{27}{3}  \\y&=9  \\\end{align}\]

Hence, the measures of \(x\) and \( y\) are \(6 \rm\, cm\) and \(9 \rm \,cm\) respectively.

(ii) What is Known?

Given figure is a parallelogram.

What is Unknown?

Values of \(x, y\)

Reasoning:

The diagonals of a parallelogram bisect each other. In a parallelogram, the opposite sides have same length.

Steps:

Property: The diagonals of a parallelogram bisect each other.

\[\begin{align}y{\rm{ }} + {\rm{ }}7{\rm{ }} &= {\rm{ }}20\\y &= 20 - 7\\y{\rm{ }} &= {\rm{ }}13\\
x{\rm{ }} + {\rm{ }}y{\rm{ }} &= {\rm{ }}16\\x{\rm{ }} + {\rm{ }}13{\rm{ }} &= {\rm{ }}16\\x{\rm{ }} &= {\rm{ }}3\end{align}\]

Hence, the measures of \(x\) and \(y\) are \(3 \rm\,cm\) and \(13 \rm\,cm \) respectively.