Question

The area of a trapezium is 850 sq. cm. One of the parallel sides is 64 cm and the
perpendicular distance between the parallel sides is 17 cm. Find the length of
other parallel side.
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Answer 1

Answer:

36cm

Step-by-step explanation:

Area of trapezium =1/2*h*(sum of parallel sides)

So 850 = 1/2*17*(64+other side)

Other side =100-64 = 36cm

Answer 2

To Find :

The other parallel side of the Trapezium .

Given :

• Area of the Trapezium = 850 cm ².

• Parallel side → $p_{1}$ = 64 cm

• height = 17 cm

We Know :

Area of a TraPezium :

$\bf{\underline{\boxed{A = \dfrac{1}{2} \times (p_{1} + p_{2}) \times h}}}$

Where :

• A = Area of the Trapezium

• $p_{1}$ = Parallel side of the Trapezium

• $p_{2}$ = Parallel side of the Trapezium

• h = Height of the Trapezium

Solution :

Let the Other parallel side be $p_{2}$.

With the given information and by Substituting the values in the formula for area of a Trapezium , we get :-

$\implies \bf{A = \dfrac{1}{2} \times (p_{1} + p_{2}) \times h} \\ \\ \\ \implies \bf{850 = \dfrac{1}{2} \times (64 + p_{2}) \times 17} \\ \\ \\ \implies \bf{850 \times 2 = (64 + p_{2}) \times 17} \\ \\ \\ \implies \bf{1700 = (64 + p_{2}) \times 17} \\ \\ \\ \implies \bf{\dfrac{1700}{17} = (64 + p_{2})} \\ \\ \\ \implies \bf{100 = (64 + p_{2})} \\ \\ \\ \implies \bf{100 - 64 = p_{2}} \\ \\ \\ \implies \bf{36 = p_{2}} \\ \\ \\ \therefore \purple{\bf{p_{2} = 36}}$

Hence , the other Parallel side of the TraPezium is 36 cm.