Square ABCD and Trapezium PQRS lie between the parallel lines l and m as shown in the figure above. If the area of the square ABCD and trapezium PQRS is equal to 64 square centimeters each, what is the length in centimeters of PQ?a)4b)8c)12d)16e)20Correct answer is option 'C'. Can you explain this answer?

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Square ABCD and Trapezium PQRS lie between the parallel lines l and m as shown in the figure above. If the area of the square ABCD and trapezium PQRS is equal to 64 square centimeters each, what is the length in centimeters of PQ?

a)
4
b)
8
c)
12
d)
16
e)
20

Correct answer is option 'C'. Can you explain this answer?

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Square ABCD and Trapezium PQRS lie between the parallel lines l and m ...

Given

Parallel lines L and M
Square ABCD and trapezium PQRS
- RS = 4 centimeters
Area of square = Area of trapezium = 64 cm

To Find: Length of PQ?

Approach

We know that Area of trapezium PQRS = ½ * (PQ + RS)* distance between parallel sides PQ and RS.
1. As we know the length of RS and the area of trapezium PQRS, we need to find the distance between the parallel lines l and m to find the value of PQ
The distance between the parallel lines is equal to the side length of the square ABCD.
1. Since we know the area of square ABCD, we can find the distance
  between the parallel lines

Working out

Area of square ABCD = 64
1. AD² = 64, i. e. AD = 8
AD = distance between parallel lines = 8
So, Area of trapezium PQRS = ½ * (PQ + RS) * distance between parallel lines
a. 64 = ½ *(PQ +4) * 8
b. PQ = 12 centimeters

Answer : C

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