The Area of trapezium of height 24.2 cm is 605 cm².one of the parrallel sides is 21 cm,find the other side.
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The Area of trapezium of height 24.2 cm is 605 cm².one of the parrallel sides is 21 cm,find the other side.
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Verified answer
Given :
[tex]~[/tex]
To Find :
[tex]~[/tex]
[tex]{\rule{190pt}{2pt}}[/tex]
SolutioN :
[tex]~[/tex]
[tex]{\bf{\dag}}[/tex] Formula Used :
[tex]\qquad\star~{\underline{\boxed{\pmb{\sf{Area_{(Trapezium)}~=~\dfrac{1}{2}~×~(Sum~of~ Parallel~Sides)~×~ Height}}}}}[/tex]
[tex]~[/tex]
[tex]{\bf{\dag}}[/tex] According to the Question :
[tex]~[/tex]
[tex]\qquad{\sf:\implies{Area_{(Trapezium)}~=~\dfrac{1}{2}~×~(a~+~b)~×~h}}[/tex]
[tex]~[/tex]
[tex]\qquad{\sf:\implies{605~=~\dfrac{1}{2}~×~(21~+~x)~×~24.2}}[/tex]
[tex]~[/tex]
[tex]\qquad{\sf:\implies{\dfrac{605~×~2}{1}~=~(21~+~x)~×~24.2}}[/tex]
[tex]~[/tex]
[tex]\qquad{\sf:\implies{\dfrac{1210}{1}~=~(21~+~x)~×~24.2}}[/tex]
[tex]~[/tex]
[tex]\qquad{\sf:\implies{1210~=~(21~+~x)~×~24.2}}[/tex]
[tex]~[/tex]
[tex]\qquad{\sf:\implies{1210~×~\dfrac{1}{24.2}~=~21~+~x}}[/tex]
[tex]~[/tex]
[tex]\qquad{\sf:\implies{\dfrac{1210~×~1}{24.2}~=~21~+~x}}[/tex]
[tex]~[/tex]
[tex]\qquad{\sf:\implies{\cancel\dfrac{1210}{24.2}~=~21~+~x}}[/tex]
[tex]~[/tex]
[tex]\qquad{\sf:\implies{50~=~21~+~x}}[/tex]
[tex]~[/tex]
[tex]\qquad{\sf:\implies{x~=~50~-~21}}[/tex]
[tex]~[/tex]
[tex]\qquad:\implies{\pmb{\underline{\boxed{\pink{\frak{x~=~29cm }}}}}}[/tex]★
[tex]~[/tex]
Hence,
[tex]~[/tex]
[tex]\qquad[/tex] ∴ The other side of trapezium is 29cm.
[tex]~[/tex]
[tex]{\rule{190pt}{2pt}}[/tex]
Step-by-step explanation:
Area of trapazium=1/2×(a+b)×height
605=1/2×24.2(a+21)
605=12.1(a+21)
605=12.1a+254.1
605-254.1/12.1=a
29=a
hope this helps you di