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if trapezium of area 140 cm horsepower sides 10 cm apart and one of them decides is 16 cm longfind the area find the length of the sother side ​

Respuesta :

Given :

  • Area of the trapezium is 140 cm².
  • Its height is 10 cm.
  • One of the parallel side is 16 cm.

To Find :

  • The other parallel side.

Solution :

  • Let the other parallel side be x

We know that,

[tex]{ \qquad \: \pmb{ \dfrac{1}{2} \times (sum \: of \: the \: parallel \: sides) \times height} = \pmb{Area_{(trapezium)}}}[/tex]

Now, Substituting the given values in the formula :

[tex]\qquad { \dashrightarrow \: { \sf{ \dfrac{1}{2} \times (16 + x)\: \times 10 \: = {140}}}}[/tex]

[tex]\qquad { \dashrightarrow \: { \sf{ 5 \times (16 + x)\ \: = {140}}}}[/tex]

[tex]\qquad { \dashrightarrow \: { \sf{ 80 + 5x = {140}}}}[/tex]

[tex]\qquad { \dashrightarrow \: { \sf{ 5x = {140 - 80}}}}[/tex]

[tex]\qquad { \dashrightarrow \: { \sf{ 5x = {60}}}}[/tex]

[tex]\qquad { \dashrightarrow \: { \sf{ x = { \dfrac{60}{5} }}}}[/tex]

[tex]\qquad { \dashrightarrow \: { \pmb{ x = { 12 }}}}[/tex]

Therefore,

  • The other parallel side of the trapezium is 12 cm.

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