Question

The ratio of the length of parallel sides of a trapezium is 2:3 . The distance between them is 16 cm . If the area of the trapezium is 320 sq. cm , find the lengths of the parallel sides ?​

Answer 1

Step-by-step explanation:

Let the length be 2x and 3x.

Height = 16cm

Area of Trapezium = 320 sq. cm

Area of Trapezium =

= 1/2 * h (a + b)

320 = 1/2*16 (2x+3x)

320 = 8*5x

320 = 40x

x = 8cm

LENGTH OF PARALLEL SIDES ARE 16 & 24 cm

Answer 2

Given :-

• The ratio of the length of parallel sides of a trapezium is 2:3 .
• The distance between them is 16 cm . If the area of the trapezium is 320 sq. cm.

To find :-

• Length of parallel sides =?

Solution :-

• Let the parallel sides be 2x and 3x.

$\qquad$ ☀️As it's given that the ratio of the length of parallel sides of a trapezium is 2:3 . Area of trapezium is 320 and the distance between parallel sides is 16 cm.

Formula used :-

$\red{\qquad\leadsto\quad \pmb {\mathfrak{Area _(trapezium) = ½ × (a + b) × h }}}$

Where :-

$\qquad$ ⎘ (a + b) is = Sum of parallel sides

$\qquad$ ⎘" h " is = Distance between parallel sides

$\qquad\small\underline{\pmb{\sf \:According \: to \: the \: question :-}}$

$\qquad\leadsto\quad \pmb {\mathfrak{Area _( Trapezium) = 320 }}$

$\pink{\qquad\leadsto\quad \pmb {\mathfrak{ ½ \times (a + b) \times h = 320 }}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ ½ \times (2x + 3x) \times 16 = 320 }}$

$\qquad\leadsto\quad \pmb {\mathfrak{ ½ \times 5x \times 16 = 320 }}$

$\qquad\leadsto\quad \pmb {\mathfrak{5x \times 8 = 320 }}$

$\qquad\leadsto\quad \pmb {\mathfrak{ 40x = 320 }}$

$\qquad\leadsto\quad \pmb {\mathfrak{ x = \cancel{\dfrac{320}{40} }}}$

$\pink{\qquad\leadsto\quad \pmb {\mathfrak{ x = 8 }}}$

$\qquad$ ⎘ First parallel side = 2x = 16cm

$\qquad$ ⎘ Second parallel side = 3x = 24cm

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