Question

The area of a trapezium is 126cm. The height of the trapezium is 7cm. If one of the bases is longer than the other by 6cm, find the length of the bases​

Answer 1

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Answer:

Length of bases are 15 cm and 21 cm.

Step-by-step explanation:

To find :-

Length of bases.

Solution :-

Given that,

Area of trapezium is 126 cm².

Height of trapezium is 7 cm.

Let, Other base be x cm.

And One base be x + 6 cm.

If the height 7 cm have two bases and height is of trapezium then the x and x + 6 are parallel sides of trapezium.

We know,

Area of trapezium = (a + b)/2 × h

Put area, height and bases (parallel sides) of trapezium in formula :

⟶ 126 = (x + x + 6)/2 × 7

⟶ 126 × 2 = 2x + 6 × 7

⟶ 252 = 2x + 6 × 7

⟶ 252/7 = 2x + 6

⟶ 36 = 2x + 6

⟶ 36 - 6 = 2x

⟶ 30 = 2x

⟶ 30/2 = x

⟶ x = 15

Length of bases :-

One base = x + 6 = 15 + 6 = 21 cm

Other base = x = 15 cm

Answer 2

Step-by-step explanation:

To find :-

Length of bases.

Solution :-

Given that,

Area of trapezium is 126 cm².

Height of trapezium is 7 cm.

Let, Other base be x cm.

And One base be x + 6 cm.

If the height 7 cm have two bases and height is of trapezium then the x and x + 6 are parallel sides of trapezium.

We know,

Area of trapezium = (a + b)/2 × h

Put area, height and bases (parallel sides) of trapezium in formula :

⟶ 126 = (x + x + 6)/2 × 7

⟶ 126 × 2 = 2x + 6 × 7

⟶ 252 = 2x + 6 × 7

⟶ 252/7 = 2x + 6

⟶ 36 = 2x + 6

⟶ 36 - 6 = 2x

⟶ 30 = 2x

⟶ 30/2 = x

⟶ x = 15

Length of bases :-

One base = x + 6 = 15 + 6 = 21 cm

Other base = x = 15 cm