Question

The area of a trapezium is 50 cm . If the ratio of parallel sides is 2:3 and the distance between the parallel sides is 10 cm, find the length of two parallel sides. ​

Answer 1

Answer:

The length of parallel sides are 4cm and 6cm.

Step-by-step explanation:

Let x and y be the lengths of the parallel sides.

Given that they are in the ratio of 2:3 i.e.,

$\frac{x}{y}$=$\frac{2}{3}$

⇒3x=2y

⇒y=$\frac{3x}{2}$----------->eqn1

wkt,

The area of Trapezium=1/2×h×(a+b)

where, a & b are the lengths of parallel sides of trapezium,

           h is the distance between these parallel sides.

Given h=10cm and Area of Trapezium=50cm.

Substituting the values in the equation

50=$\frac{1}{2}$×10×(x+$\frac{3x}{2}$)        ∵from eqn1

⇒50=5×($\frac{2x+3x}{2}$)

⇒10×2=5x

⇒x=20/5

⇒x=4

put x=4 in eqn1

y=$\frac{3*4}{2}$

⇒y=6

Answer 2

Answer:

4 cm and 6 cm

Step-by-step explanation:

$area \: of \: trapezium = 50 \: {cm}^{2} \\ let \: parallel \: side \: be \: \: \: \: a \: \: \: \: \: \: \: \: and \: \: \: b \: \: \: \: \: \: \: and \: \\ distance \: between \: them \: is \: \: \: h \\ then \\ a : b = 2 : 3 \\ let \: rational \: constant = x \\ then \: a = 2x \: and \: b \: = 3x \\ \\ and \: h \: = 10 \: cm \: given \: \\ according \: to \: question \\ \frac{1}{2} h(a + b) = 50 \\ \frac{1}{2} \times 10 \times (2x + 3x) = 50 \\ 5x = \frac{50}{5} \\ x = \frac{10}{5} \\ x = 2 \\ so \: a = 2x = 2 \times 2 = 4 \: cm \\ b = 3x = 3 \times 2 = 6 \: cm$

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