Question

The parallel sides of the trapezium are 7 more and 7 less than the distance between them.Find their lengths and the distance between them, If the area of the Trapezium is 169 m square.
Answer: Parallel sides are 20m and 6m respectively.Distance between parallel sides is 13m.
Explain me How????

Answer 1

Let the distance between parallel sides be x

According to question One parallel side is 7 more than the distance = x + 7

and another parallel line is 7 less than the distance = x - 7

We know area of Trapezium

= 1/2 (Sum of parallel sides) × distance between them

Here Area given = 169 m²

∴1/2 (Sum of parallel sides) × Distance between them = 169 m²

Putting values

1/2 [(x + 7) + (x - 7)] × x = 169

1/2 × 2x × x = 169

x² = 169

x² = 13²

x = 13

∴ Distance between parallel Sides is 13 m.

One of the Parallel side = x + 7 = 13 + 7 = 20 m

Another Parallel side = x - 7 = 13 - 7 = 6 m

Answer 2

Solution :

Let the distance between two

parallel sides in a Trapezium = h m

a , b are two parallel sides .

a = ( h + 7 ) m

b = ( h - 7 ) m

According to the problem given ,

area = 169 m²

=> [( a + b )h]/2 = 169

=> [(h+7+ h-7)h]/2 = 169

=> [ 2h² ]/2 = 169

=> h² = 169

=> h = √169

=> h = √13²

=> h = 13 m

Therefore ,

distance between the parallel

sides = h = 13 m

a = h + 7 = 13 + 7 = 20m

b = h - 7 = 13 - 7 = 6m

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