Question

The area of a trapezium is 336 sq. cm. If its parallel sides are in the ratio 5 : 7 and the perpendicular distance between them be 14 cm, then the smaller of parallel sides is (i) 20 cm (in) 22 cm (in) 24 cm​

Answer 1

Answer:

A Option is the right option.

20cm

Formula :

Area of Trapezium = 1/2 × sum of parallel sides × height

Explanation:

Let the ratio of parallel sides =  5x:7x  

⇒ 336 = (5x+7x) × 14  

⇒ 336 × 2/14 = 12x  

⇒48 = 12x  

⇒ x = 48/12  

⇒ x = 4

Therefore,

Smaller side of trapezium = 5 × 4 = 20cm

Answer 2

To find : smaller side of parallel sides of trapezium .

Given : The area of a trapezium is $336 \ cm^{2}$ .Parallel sides are in the ratio $5 : 7$  and the perpendicular distance between them be $14$ cm .

Solution :

• As per given data we know that area of a trapezium is $336 \ cm^{2}$ .Parallel sides are in the ratio $5 : 7$  and the perpendicular distance between them be $14$ cm .
• Let , $5x$ and $7x$ be the parallel sides in the ratio .
• Area of trapezium = $\frac{1}{2} \times (sum\ of \ parallel \ sides ) \times height$

       $336 = \frac{1}{2}\times (5x + 7x )\times 14 \\336 = 12x \times 7 \\12x =\frac{336}{7} \\x =\frac{48}{12} \\x = 4$

• Now , parallel sides are :

       $5x =5\times 4 =20\ cm \\7x = 7\times 4 = 28\ cm$

Hence , smaller of parallel sides is $20\ cm$ .Therefore , option (i) $20\ cm$ is correct  .