Question

the parallel sides of trapezium are in the ratio 5: 7. If the distance between the parallel sides is 24cm and its area is 720cm².finde the length of other parallel side​

Answer 1

Given that , Parallel sides of trapezium are in the ratio ( a : b ) 5: 7 , Distance btwn parallel sides is 18 cm & Area of Trapezium is 540 cm² .

Exigency To Find : The parallel sides of Trapezium .

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⠀⠀ Let's Consider parallel sides of Trapezium be 5x cm and 7x cm , respectively . As it is , Parallel sides of trapezium are in the ratio 5: 7 .

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

Where ,

• h , Hieght of the Trapezium or Distance btwn parallel sides &
• a & b , Parallel Sides of Trapezium .

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

$\sf \dashrightarrow \:\:Area_{(\:Trapezium \:)}\:\:=\:\dfrac{ \: 1 }{2} \times h \:\big( \: a + b\:\big)\:  \:\: \\\\\sf \dashrightarrow \:\:540\:\:=\:\dfrac{ \: 1 }{2} \times 18 \:\big( \: 5x + 7x \:\big)\:  \:\:\\\\\sf \dashrightarrow \:\:540\:\:=\:9\:\big( \: 5x + 7x \:\big)\:  \:\: \\\\\sf \dashrightarrow \:\:540\:\:=\:9 \times \: 12x \:  \:\: \\\\\sf \dashrightarrow \:\:\cancel{\dfrac{540}{9}}\:\:=\: 12x \:  \:\:\\\\\sf \dashrightarrow \: 12x \:  =\: 60 \: \\\\\sf \dashrightarrow \:\:x\:\:=\:   \:\cancel{\dfrac{60}{12}}\\\\\pmb {\underline {\boxed {\purple {\:\frak{ \:x\:\:=\:5\:cm\:}}}}}\:\bigstar \:$

Therefore ,

• a , First Parallel side of Trapezium : 5x = 5 × 5 = 25 cm &
• b , Second Parallel side of Trapezium : 7x = 7 × 5 = 35 cm .

⠀

∴ Hence, Parallel Sides of Trapezium are 25 cm and 35 cm , respectively .