Question

Thea area of a trapezoidal field is 416 m 2 and one of the parallel side is 8m
longer than the other side. If the distance between the parallel sides is 13 m, find
the length of the two parallel sides.

Answer 1

Answer:

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Answer 2

Question :

The area of a trapezoidal field is 416 m 2 and one of the parallel side is 8m

longer than the other side. If the distance between the parallel sides is 13 m, find

the length of the two parallel sides.

Answer :

$\sf\pink{Given:}$

• Area of the trapezoidal field is 416 m²

• One of the parallel side is 8 m longer than the other .

• Distance between the parallel sides is 13 cm .

$\sf\pink{To\:Find:}$

• Length of the two parallel sides .

Explanation :

• Let one side be "x" m

• Therefore the other side is x + 8 .

$\bf\purple{Area\:Of\: Trapezium = 2\times(a + b)\times h}$

• a is length of one of the parallel side that is x m.

• b is length of the other parallel side is x + 8 m

• h is the height that is 13 m

$\longrightarrow\bf{ 416 = 2\times (x + x + 8)\times 13}$

$\longrightarrow\bf{ 416 = 2\times (2x + 8)\times 13}$

$\longrightarrow\bf{ 416 = (4x + 16)\times 13}$

$\longrightarrow\bf{ 416 = 52x + 208 }$

$\longrightarrow\bf{ 416 - 208 = 52x }$

$\longrightarrow\bf{ 208 = 52x }$

$\longrightarrow\bf{ x = \dfrac{208}{52} }$

$\longrightarrow\bf\red{ x = 4}$

• Therefore length of one side is x m

$\longrightarrow\bf\red{ x = 4\:m}$

• Therefore length of other side is x + 8

$\longrightarrow\bf{ 4 + 8}$

$\longrightarrow\bf\red{ 12\:m}$