the area of a tripezium is 686 cm square if one of the parallel side exceeds the other by 7 cm and the distance between the parallel side is 28 cm find the other parallel side of the tripezium
Answers
Given:-
Area of trapezium = 686cm²
One of the parallel side exceeds other by 7cm.
Distance between the parallel sides = 28cm
Solution:-
Let the parallel side be x.
So the other parallel side will be (x + 7)cm
We know that,
\bullet\quad\boxed{\rm Area \ of \ Trapezium = \dfrac{1}{2}(sum \ of \ parallel \ sides)(distance \ between \ parallel \ sides)}∙Area of Trapezium=21(sum of parallel sides)(distance between parallel sides)
Hence,
\rm 686cm^2 = \dfrac{1}{2}[(x+7)cm+x \ cm](28cm)686cm2=21[(x+7)cm+x cm](28cm)
\rm \dashrightarrow 686cm^2 = \dfrac{[(2x +7) cm](28cm)}{2}⇢686cm2=2[(2x+7)cm](28cm)
\rm \dashrightarrow 686cm^2 =(2x+7)cm14cm⇢686cm2=(2x+7)cm14cm
\rm \dashrightarrow \dfrac{686cm^2}{14cm} =(2x+7)cm⇢14cm686cm2=(2x+7)cm
\rm \dashrightarrow 49cm =(2x+7)cm⇢49cm=(2x+7)cm
\rm \dashrightarrow 49cm - 7cm =2x⇢49cm−7cm=2x
\rm \dashrightarrow 42cm =2x⇢42cm=2x
\rm \dashrightarrow \dfrac{42cm}{2}=x⇢242cm=x
\bf\dashrightarrow x = 21cm⇢x=21cm
• Parallel side = x = 21cm
• Other Parallel side = x + 7 = 21 + 7 = 28cm.