Question

the area of trapezium is 168 cm sq. and its height is 8 cm.if one of the parallel sides is longer than the other by 8 cm,find the length of two parallel sides.​

Answer 1

Step-by-step explanation:

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Answer 2

✬ Parallel Sides = 17 cm & 25 cm ✬

Step-by-step explanation:

Given:

• The area of trapezium is 168 cm².
• Height of trapezium is 8 cm.
• One parallel side is 8 cm longer than another parallel side.

To Find:

• What is meaure of both parallel sides ?

Solution: In trapezium ABCD ,Let the measure of one parallel side be x cm. We have

• AB || CD
• AB = x cm therefore CD = x + 8 cm
• AC = 8 cm ( Height )

We know that the :-

★ Area of Trapezium = 1/2 $\times$ Height ( Sum of parallel sides ) ★

A/q

• Area = 168 cm²

$\implies{\rm }$ Area of ABCD = 1/2 $\times$ AE $\times$ ( AB + CD )

$\implies{\rm }$ 168 = 1/2 $\times$ 8 $\times$ ( x + x + 8 )

$\implies{\rm }$ 168 = 4 $\times$ ( 2x + 8 )

$\implies{\rm }$ 168 = 8x + 32

$\implies{\rm }$ 168 – 32 = 8x

$\implies{\rm }$ 136 = 8x

$\implies{\rm }$ 136/8 = x

$\implies{\rm }$ 17 cm = x

So, Measure of parallel sides of trapezium are

➩ AB = x = 17 cm

➩ CD = x + 8 = 17 + 8 = 25 cm

____________________

★ Verification ★

➟ 168 = 1/2 $\times$ AE $\times$ ( AB + CD )

➟ 168 = 1/2 $\times$ 8 $\times$ ( 17 + 25 )

➟ 168 = 4 $\times$ 42

➟ 168 = 168

[ Verified ]