Question

2. The parallel sides of a trapezium are in the ratio 6 : 7 and the distance between
them is 12.5 cm. Find the lengths of sides if the area is 6.50 m².
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Answer 1

Given :-

Ratio of two parallel sides of a trapezium = 6 : 7

Distance between them = 12.5 cm

Area of the trapezium = 6.50 m²

To Find :-

The lengths of sides.

Analysis :-

Consider the common ratio as a variable.

Multiply each side to the variable given.

Substitute the values in it's respective formula and find the value of the variable accordingly.

Substitute it's value in both the sides.

Solution :-

We know that,

• l = Length
• a = Area
• s = Side
• h = Height

Let the sides be 6x and 7x.

By the formula,

$\underline{\boxed{\sf Area \ of \ trapezium=\dfrac{1}{2} \times (a+b)h}}$

Given that,

Area (a) = 6.50 m² = 65000 cm²

Height (h) = 12.5 cm

Substituting their values,

65000 = 1/2 (6x + 7x) 12.5

65000 = 12.5 (13x)/2

12.5 × 13x = 65000 × 2

13x = 130000/12.5

13x = 10400

x = 10400/13

x = 800

The sides would be,

6x = 6 × 800 = 4800 cm

7x = 7 × 800 = 5600 cm

Therefore, the length of the sides are 4800 cm and 5600 cm.