Question

the area of the trapezium is 210cm^2 and its height is 14 cm if one of the parallel sides is longer than the other by 6cm find the two parallel sides​

Answer 1

Please find the attached photograph for your answer

Answer 2

Given : The area of the trapezium is 210 cm² and its height is 14 cm if one of the parallel sides is longer than the other by 6cm .

Need To Find : The two parallel sides.

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❍ Let's consider the Length of one parallel be x cm .

Given that ,

⠀⠀⠀⠀One of the parallel sides is longer than the other by 6cm .

⠀⠀⠀⠀$\therefore$ Length of other parallel side is ( x + 6 ) cm

$\frak{\underline { As, \;We\;Know \:that\::}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ $\pink {\boxed {\sf{ Area_{(Trapezium)} =\dfrac{1}{2} \times h \:\times (a + b) }}}$

⠀⠀⠀⠀Here h is the Height of Trapezium in metres and a & b are the two parallel sides of Trapezium in metres and we are given with the Area of Trapezium is 210 cm² .

⠀⠀⠀⠀⠀⠀$\underline {\sf{\bf{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}}$

⠀⠀⠀⠀⠀⠀⠀$:\implies { \sf{ 210cm^{2} = \dfrac{1}{2} \times 14 \times ( x + x + 6 ) }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀$:\implies { \sf{ 210cm^{2} = \dfrac{1}{\cancel {2}} \times \cancel {14} \times ( x + x + 6 ) }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$:\implies { \sf{ 210cm^{2} = 7 \times ( x + x + 6 ) }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$:\implies { \sf{210cm^{2} = 7 \times (2x + 6 ) }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$:\implies { \sf{210cm^{2} = 14x + 42 }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$:\implies { \sf{210 - 42 = 14x }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀ $:\implies { \sf{168 = 14x }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ $:\implies { \sf{ \dfrac{\cancel {168}}{\cancel {14}} = x }}$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  x = 12 \: cm}}}}\:\bf{\bigstar}$

Therefore,

• Length of one Parallel sides of Trapezium is x = 12 cm

• Length of other Parallel sides of Trapezium is ( x + 6 ) = 12 +6 = 18 cm .

Therefore,

⠀⠀⠀⠀⠀$\underline {\therefore\:{\pink{ \mathrm { Hence,\: Length\:of\:two\:parallel \:sides\:of\:Trapezium \:are\:12cm\:and\:18cm\: . }}}}$

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$\qquad\quad\boxed{\bf{\mid{\overline{\underline{\blue{\bigstar\: Verification \: :}}}}}\mid}$

$\frak{\underline { As, \;We\;Know \:that\::}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ $\pink {\boxed {\sf{ Area_{(Trapezium)} =\dfrac{1}{2} \times h \:\times (a + b) }}}$

⠀⠀⠀⠀Here h is the Height of Trapezium in metres and a & b are the two parallel sides of Trapezium in metres and we are given with the Area of Trapezium is 210 cm² .

⠀⠀⠀⠀⠀⠀$\underline {\sf{\bf{\star\:Now \: By \: Substituting \: the \: Given \:and\:Found \:Values \::}}}$

⠀⠀⠀⠀⠀⠀⠀$:\implies { \sf{ 210cm^{2} = \dfrac{1}{2} \times 14 \times ( 12 + 18 ) }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀$:\implies { \sf{ 210cm^{2} = \dfrac{1}{\cancel {2}} \times \cancel {14} \times ( 12 + 18 ) }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$:\implies { \sf{ 210cm^{2} = 7 \times ( 12 + 18 ) }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$:\implies { \sf{ 210cm^{2} = 7 \times 30 }}$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  210cm^{2} = 210 \: cm^{2}}}}}\:\bf{\bigstar}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\therefore {\underline {\sf{\bf{ Hence \:Verified \:}}}}$

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