Question

the area of a trapiziun field is 780m²
the perpendicular distance between
the two parrellel sides is 24m. If 1
parrellel sides exsits the other by 15m
find the length of the parrllel sides ​

Answer 1

Question :

The area of a Trapezium field is 780m² , the perpendicular distance between the two parallel sides is 24m. If one parallel sides exceeds the other by 15 m, find the length of the parallel sides .

Given :

• Area of the Trapezium = 780 cm²

• Distance between the parallel sides = 24 m.

• Length of one parallel side = Other parallel side + 15 m.

To find :

The length of the two parallel sides .

Solution :

Let the one of the parallel side be x.

So according to the Question, the other parallel side of the Trapezium will be (x + 15) m.

We know the formula for area of a Trapezium, i.e

$\bf{A = \dfrac{1}{2} \times Sum\:of\:parallel\:sides \times distance\:between \:the\:parallel\:sides}$

Now , using the formula and substituting the values in it, we get :

$:\implies \bf{A = \dfrac{1}{2} \times (p_{1} + p_{2}) \times h}$

Where,

• p = Parallel side
• h = Height

$:\implies \bf{780 = \dfrac{1}{2} \times [x + (x + 15)] \times 24 h}$

$:\implies \bf{780 = \dfrac{1}{2} \times (2x + 15) \times 24}$

$:\implies \bf{780 = (2x + 15) \times 12}$

$:\implies \bf{65 = (2x + 15)}$

$:\implies \bf{65 - 15 = 2x}$

$:\implies \bf{50 = 2x}$

$:\implies \bf{\dfrac{50}{2} = 2x}$

$:\implies \bf{25 = 2x}$

$\boxed{\therefore \bf{Parallel\:Side\:(x) = 25\:m}}$

Hence, the First parallel side is 25 (since we have taken one of the parallel side as x) and other parallel is (25 + 15) i.e, 40 m.