Question

The parallel sides of a trapezium are in the ratio 3: 7. Find their lengths, if the trapezium is of height 12 cm and has area 60 cm 2 .

Answer 1

Step-by-step explanation:

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Answer 2

$\bf \underline{ \sf \: Given : }$

• Parallel sides are in the ratio 3:7

• Height = 12 cm

• Area = 60 cm^2

$\bf \underline{ \sf \: To \: Find : }$

• The lengths of the parallel sides

$\bf \underline{ \sf Solution :}$

Let the parallel sides of trapezium be 3x and 7x and denote it by a and b

${ \boxed {\large{ \purple{ \sf \: Area \: of \: Trapezium = \dfrac{1}{2}(a + b) \times h }}}}$

$\longrightarrow \sf 60 = \dfrac{1}{2} (3x + 7x) \times 12$

$\longrightarrow \sf 60 = \dfrac{1}{2} \times 10x \times 12$

$\longrightarrow \sf 60 = \dfrac{120x}{2}$

$\longrightarrow \sf 60 = \dfrac{120x}{2}$

$\longrightarrow \sf x = \dfrac{60 \times 2}{120}$

$\longrightarrow \sf x = \dfrac{120}{120}$

$\longrightarrow \sf x = \boxed{ \sf \: 1}$

Hence,

$\star \rm \: One \: parallel \: side = 3x = 3 \: cm$

$\star \rm \: Other \: parallel \: side = 7x = 7\: cm$

VeRiFiCaTiOn :

${ \boxed {\large{ \purple{ \sf \: Area \: of \: Trapezium = \dfrac{1}{2}(a + b) \times h }}}}$

$\longrightarrow \sf 60 = \dfrac{1}{2} (7 + 3) \times 12$

$\longrightarrow \sf 60 = \dfrac{1}{ 2} \times 10 \times 12$

$\longrightarrow \sf 60 = \dfrac{120}{ 2}$

$\longrightarrow \sf 60 = 60$

Hence,Verified!!