The area of trapezium is 686 cm!. If one of the parallel sides exceeds the other by 7cm and the distance between the parallel sides is 28cm, find the other parallel side of the trapezium.
Answers
Step-by-step explanation:
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=
2
1
(sum of parallel sides)(distance between parallel sides)
Hence,
\rm 686cm^2 = \dfrac{1}{2}[(x+7)cm+x \ cm](28cm)686cm
2
=
2
1
[(x+7)cm+x cm](28cm)
\rm \dashrightarrow 686cm^2 = \dfrac{[(2x +7) cm](28cm)}{2}⇢686cm
2
=
2
[(2x+7)cm](28cm)
\rm \dashrightarrow 686cm^2 =(2x+7)cm14cm⇢686cm
2
=(2x+7)cm14cm
\rm \dashrightarrow \dfrac{686cm^2}{14cm} =(2x+7)cm⇢
14cm
686cm
2
=(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⇢
2
42cm
=x
\bf\dashrightarrow x = 21cm⇢x=21cm
• Parallel side = x = 21cm
• Other Parallel side = x + 7 = 21 + 7 = 28cm.
Answer:
the other parallel side of trapezium in 28cm