Question

8. The area of trapezium is 640 cm². If its parallel sides are in the ratio 2 : 3 and the perpendicular distance between the two is 16 cm, find length of each parallel side.​

Answer 1

Given:

• The area of trapezium is 640 cm². If its parallel sides are in the ratio 2 : 3 and the perpendicular distance between the two is 16 cm

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To Find:

• Length of Parrallel sides

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Solution:

• Let Parrallel sides be 2x and 3x
• a = 2x , b = 3x

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Height of trapezium = 16cm

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${ \pink{ \star}} \: { \underline{ \boxed{ \bold{ \sf{ \color{blue}{Area \: of \: Trapezium = \frac{1}{2} \times h \times (a + b)}}}}}} \: { \pink{ \star}}$

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Putting values in the formula:

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$: \implies \tt640 = \dfrac{1}{2} \times 16 \times (2x + 3x) \\ \\ \\ : \implies \tt640 = 1 \times 8 \times 5x \\ \\ \\ : \implies \tt640 = 8 \times 5x \\ \\ \\ : \implies \tt \frac{640}{8} = 5x \\ \\ \\ : \implies \tt80 = 5x \\ \\ \\ : \implies \tt x = \frac{80}{5} \\ \\ \\ : \implies{ \boxed{ \color{green}{ \frak{ x = 16cm}}} \: { \red{ \bigstar}}}$

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Parrallel sides are:

• a = 2x = 2 × 16 = 32cm
• b = 3x = 3 × 16 = 48cm

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$\therefore { \red { \underline{\sf{The \: Parrallel \: sides \: of \: trapezium \: are \: 32 \: and \: 48cm }}}}$

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Answer 2

☀️  Given that,  area of trapezium is 640 cm². If its parallel sides are in the ratio 2 : 3 and the perpendicular distance between the two is 16 cm.

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Let's say that,

Parallel sides of the Trapezium are 2x and 3x

❍ To calculate the length of each parallel side we must know that ::

• Area of Trapezium = 1/2 × ( Sum of parallel sides ) × h

Where,

h is distance between the parallel sides [ height ]

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T H E R E F O R E,

⤳  640 = 1/2 × ( 2x + 3x ) × 16

⤳  640 = ( 2x + 3x ) × 8

⤳  ( 2x + 3x ) = 640/8

⤳  ( 2x + 3x ) = 80

⤳  5x = 80

⤳  x = 80/5

⤳  x = 16

Finding Sides :-

• 2x = 2 × 16 = 32 cm

• 3x = 3 × 16 = 48 cm

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