Question

The area of a trapezium is 1620 cm2 it's parallel sides are in the ratio 4:5 and the distance between them is 36 cm find the length of each of the parallel sides

Answer 1

Diagram:

$\setlength{\unitlength}{1cm} \begin{picture}(6,6) \put(1, 2){\line(1,1){3}} \put(1, 2){\line(1, 0){3}} \put(4,2){\line(1, 1){3}} \put(4,5){\line(1,0){3}} \put(4, 2){\line(0, 1){3}} \put(4.2, 2){\sf B} \put(0.8,2){\sf A} \put(7,5){\sf C} \put(4,5){\sf D} \put(4.1,3){\sf h} \put(5,5){\sf 40cm}\put(2,1.7){\sf 50cm} \put(4,3.4){\sf 36cm} \end{picture}$

Given:

• Area of Trapezium = 1620cm²
• Ratio of parallel sides = 4:5
• Distance between parallel sides = 36cm

Find:

• Length of each parallel side

Solution:

Let, the f1st parallel side be 4x cm

and 2nd parallel side be 5x cm

we, know that

$\boxed{\rm Area \: of \: trapezium = \dfrac{1}{2}( p_{1} +p_{2}) \times h }$

where,

• $\rm p_1 = 4x\: cm$
• $\rm p_2 = 5x \: cm$
• Distance between parallel sides = 36cm
• Area of Trapezium = 1620cm²

So,

$\dashrightarrow\rm Area \: of \: trapezium = \dfrac{1}{2}( p_{1} +p_{2}) \times h$

$\dashrightarrow\rm 1620 = \dfrac{1}{2}( 4x +5x) \times 36$

$\dashrightarrow\rm 1620 = \dfrac{1}{2}( 9x) \times 36$

$\dashrightarrow\rm 1620 = \dfrac{324x}{2}$

$\dashrightarrow\rm 1620 = 162x$

$\dashrightarrow\rm \dfrac{1620}{162} = x$

$\dashrightarrow\rm x = 10cm$

Now,

F1st parallel side = 4x = 4×10 = 40cm

2nd parallel side = 5x = 5×10 = 50cm

Answer 2

Answer:

its answer is 40 cm.and 50 cm