Question

17. The distance between the parallel sides of a trapezium which are in the ratio 3 : 5 is 22 cm. If the area of
the trapezium is 1100 cm”, find the parallel sides of the trapezium.
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Answer 1

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Q) The distance between the parallel sides of a trapezium which are in the ratio 3 : 5 is 22 cm . If the area of the trapezium is 1100 cm² , Find the parallel sides of the trapezium .

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✯ Given :–

• Ratio of parallel sides = 3:5
• Height = 22 cm
• Area of trapezium = 1100 cm²

✯ To Find :–

• The length of parallel sides .

✯ Solution :–

Let the ratios be 3x & 5x .

So ,

• Parallel sides = 3x & 5x

Now , Using the Formula to find area

$\boxed{ \sf{area = \frac{1}{2} (sum \: of \: parallel \: sides) \times height}}$

put the values ..

$\mapsto \rm \: 1100 \: \cancel{cm}^{2} = \frac{1}{ \cancel2} (3x + 5x) \cancel{22 }\: \cancel{cm}$

$\mapsto \rm \: \cancel{1100} \: cm = (8x) \cancel{11}$

$\mapsto \rm \: 8x = 100 \: cm$

$\mapsto \underline{ \boxed{ \rm{ \red{x = 12.5 \: cm}}}}$

So ,

$\rm \: the \: parallel \: sides \: would \: be : \\ \rightarrow \rm \boxed{ \underline{ \rm \purple{3x = 3 \times 12.5 \: cm = 37.5 \: cm}}} \\ \rm \: and \\ \rightarrow \boxed{ \underline{ \rm \: \pink{5x = 12.5 \times 5 \: cm = 62.5 \: cm}}}$

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✯ Know More :–

• Trapezium is a Quadrilateral .
• Perimeter of trapezium = sum of all sides .
• Area of trapezium = $\dfrac{1}{2}$ (sum of parallel sides) × height .
• Unit of area = unit²
• Unit of Perimeter = unit