Question

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

Answer 1

Step-by-step explanation:

Area=1/2(a+b)×h

900=1/2(x+2x)×24

900=(3x/2)×24

900=36x

X=900/36

X=25cm

and the other side is 2x=2×25=50cm

Answer 2

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's assume the length of the two parallel sides be x and 2x.

As we know that,

$\star \: {\underline{\boxed{\mathcal{\pmb{\quad Area \: of \: the \: Trapezium = \frac{sum \: of \: parallel \: sides}{2} \times distance \: between \: them}}}}}$

Substituting values;

$:\implies\sf{ \frac{x + 2x}{2} \times 24 = 900} \\ \\ :\implies\sf{ \frac{3x}{2} \times 24 = 900} \\ \\ :\implies\sf{3x \times 12 = 900} \\ \\ :\implies\sf{3x = \frac{\cancel{900}}{\cancel{12}}} \\ \\ :\implies\sf{3x = 75} \\ \\ :\implies\sf{x = \frac{\cancel{75}}{\cancel{3}}} \\ \\ :\implies{\boxed{\sf{\gray{x = 25} \: \bigstar}}}$

Now,

• Length of 1 parallel side = x = 25 cm

• Length of other parallel sides = 2x = 2 × 25 = 50 cm

Henceforth;

• The length of other two sides are 25cm and 50cm.