Question

The ratio of the length of the parallel sides of a trapezium is 3 2 the shortest distance between them is 15 cm if the area of the trapezium is 450 cm ^2 the sum of the length of the parallel sides is

Answer 1

here is your answer...

Answer 2

The sum of the length of the parallel sides is 60 cm

Correct question : The ratio of the length of the parallel sides of a trapezium is 3 : 2 , the shortest distance between them is 15 cm , the area of the trapezium is 450 cm² the sum of the length of the parallel sides is

Given :

• The ratio of the length of the parallel sides of a trapezium is 3 : 2

• The shortest distance between them is 15 cm

• The area of the trapezium is 450 cm²

To find :

The sum of the length of the parallel sides

Solution :

Step 1 of 3 :

Form the equation to find the length of the parallel sides

Here it is given that ratio of the length of the parallel sides of a trapezium is 3 : 2

Let length of the parallel sides are 3x cm and 2x cm

Now shortest distance between them is 15 cm

Area of trapezium

$\displaystyle \sf = \frac{1}{2} \times Sum \: of \: parallel \: sides \times Distance \: between \: parallel \: sides$

$\displaystyle \sf = \frac{1}{2} \times (3x + 2x) \times 15 \: \: {cm}^{2}$

$\displaystyle \sf = \frac{1}{2} \times 5x \times 15 \: \: {cm}^{2}$

$\displaystyle \sf = \frac{75x}{2} \: \: {cm}^{2}$

Since area of the trapezium is 450 cm²

So by the given condition

$\displaystyle \sf \frac{75x}{2} = 450$

Step 2 of 3 :

Calculate length of the parallel sides

$\displaystyle \sf \frac{75x}{2} = 450$

$\displaystyle \sf{ \implies }x = 450 \times \frac{2}{75}$

$\displaystyle \sf{ \implies }x = 12$

∴ Length of the parallel sides are 36 cm and 24 cm

Step 3 of 3 :

Calculate sum of the length of the parallel sides

Since length of the parallel sides are 36 cm and 24 cm

∴ Sum of the length of the parallel sides

= 36 cm + 24 cm

= 60 cm

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