Question

The lengths of the parallel sides.
of trapezium
ratio 3:5 and the distance between
them is 10cm. if the area of
trapezium is 120cm²
find the length of
parallel sides.
​​

Answer 1

Answer:

Length of parallel sides are in ratio 3:5.

Let the larger side =5x

⇒ Smaller side =3x

h=10 cm

$\sf \: Area  \: of \: trapezium= \frac{1}{2}  (Sum \: of \: parallel \: sides)× (height)$

$\sf \: area \: of \: trapezium = \frac{1}{2} \times (3x + 5x) \times 10$

$\sf \implies 120= \frac{1}{2} \times 8x \times 10$

$\sf \implies \: 120 = 1 \times 8x \times 5$

$\sf \implies \: \cancel\frac{120}{5} =8x$

$\sf \implies \: 24 = 8x$

$\sf \implies \: x = \cancel\frac{24}{8}$

$\sf \implies \: x = 3$

Paralell sides = 9 and 15 cm

Answer 2

Given that , The lengths of the parallel sides of trapezium are in ratio 3:5 and the distance between them is 10cm & the area of Trapezium is 120 cm² .

Exigency To Find : The Length of Parallel sides ?

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

❍ Let's Consider the Length of Parallel sides be 3x cm & 5x cm , respectively.

As , We know that ,

⠀⠀⠀⠀⠀▪︎⠀Formula for Area of Trapezium :

$\qquad \star \:\:\underline {\boxed {\pink{\pmb{\frak{ \:\:Area _{(\:Trapezium \:)}\: \:=\:\dfrac{1}{2} \:\times h \: \times \{ a + b \}\: \:sq.\:units\:}}}}}$

⠀⠀⠀⠀⠀Here , h is the Distance between parallel sides of Trapezium [ or Height ] , a & b are the two parallel sides of Trapezium & Area of Trapezium is 120 cm² .

$\qquad \dashrightarrow \sf \:\:Area _{(\:Trapezium \:)}\: \:=\:\dfrac{1}{2} \:\times h \: \times \{ a + b \}\:$

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad \dashrightarrow \sf \:\:Area _{(\:Trapezium \:)}\: \:=\:\dfrac{1}{2} \:\times h \: \times \{ a + b \}\:$

$\qquad \dashrightarrow \sf \:\:120\: \:=\:\dfrac{1}{2} \:\times 10 \: \times \{ 5x + 3x \}\:$

$\qquad \dashrightarrow \sf \:\:120\:\times \:2 \:=\: 10 \: \times \{ 5x + 3x \}\:$

$\qquad \dashrightarrow \sf \:\:240 \:=\: 10 \: \times \{ 5x + 3x \}\:$

$\qquad \dashrightarrow \sf \:\:\dfrac{240}{10} \:=\: \{ 5x + 3x \}\:$

$\qquad \dashrightarrow \sf \:\:24 \:=\: \{ 5x + 3x \}\:$

$\qquad \dashrightarrow \sf \:\:24 \:=\: 5x + 3x \:$

$\qquad \dashrightarrow \sf \:\:8x \:=\: 24\:$

$\qquad \dashrightarrow \sf \:\:x \:=\: \dfrac{ 24}{8}\:$

$\qquad \dashrightarrow \sf \:\:x \:=\: 3\:$

$\qquad \dashrightarrow \underline {\boxed {\pmb{\frak{ \purple { \:x \:=\:3 \:cm \:}}}}}$

Therefore,

• The Length of First parallel sides is 3x = 3(3) = 9 cm &
• The Length of Second Parallel sides is 5x = 5(3) = 15 cm .

$\qquad \therefore \:\underline {\sf Hence, \:The \:Length \:of \:Parallel \:sides \:of \:Trapezium \:are \:\pmb{\bf 9 \:cm \:\& \:15 \:cm \:}\:, respectively \:.\:}$