Question

The area of trapezium is 900sq.cm the distance between the parallel sides is 24 cm if one of the parallel sides is double the other find the length of the two parallel sides

Answer 1

GIVEN :-

• Area of the trapezium = 900 cm²

• Distance between the parallel sides = 24 cm

• One of the parallel sides is double the other .

TO FIND :-

• Length of the two parallel sides .

SOLUTION :-

 Let the two parallel sides be x and 2x .

  $\bf Area \ of \ trapezium = \dfrac{Sum \ of \ parallel \ sides }{2} \times Distance \ between \ them$

   $\longrightarrow\sf \dfrac{x+2x}{2}\times 24 = 900\\\\\longrightarrow \dfrac{3x}{2}\times 24 = 900 \\\\\longrightarrow 3x\times 12 = 900 \\\\\longrightarrow 3x = 75 \\\\\longrightarrow x = 25$

Length of one parallel sides , x = 25 cm

Length of other parallel sides , 2x = 50 cm  

Answer 2

● Answer -

a = 25 cm

b = 50 cm

● Explanation -

GIVEN :-

Area of a Trapezium :-900 $cm^{2}$

Height of a trapezium :- 24 cm

ALSO GIVEN,

b = 2a

TO FIND :-

length of two parallel sides

SOLUTION :-

$\bf \red{Area \:of \:trapezium} =\huge\frac{height \times ( a + b)}{2}$

$\implies \bf a = parallel\: side$

$\implies \bf b = another \:parallel\: side$

$\implies \bf 900 =\frac{(a+ 2a) \times 24}{2}$

$\implies\bf 900 = 3a\times12$

$\implies\bf \frac{900}{12} = 3a$

$\implies \bf 75 = 3a$

$\implies\bf \frac{75}{3} = a$

$\implies\bf 25 = a$

Length of 1 parallel side = 25 cm

length of another parallel side = 50 cm