Question

1. Ratio of length of parallel sides of a trapezium is 2:3. Distance
between them is 16cm. If the area of trapezium is 320cm² Find
length of parallel sides​

Answer 1

Given

• Ratio of length of parallel sides of a trapezium is 2:3. Distance between them is 16cm. If the area of trapezium is 320cm²

To find

• Length of parallel sides

Solution

✰ Ratio of length of parallel sides = 2 : 3

✰ Distance between parallel sides = 16 cm

✰ Area of trapezium = 320 cm²

• Let the parallel sides be 2x and 3x

$\\{\underline{\boxed{\bf{\red{Area\:of\:trapezium=\dfrac{1}{2}\times{(a+b)}\times{h}}}}}}$

$\implies\sf 320 = \dfrac{1}{2}\times{(2x+3x)}\times{16}$

$\implies\sf 320=\dfrac{1}{2}\times{5x}\times{16}$

$\implies\sf 320=5x\times{8}$

$\implies\sf \dfrac{320}{8}=5x$

$\implies\sf 40=5x$

$\implies\sf x=\cancel\dfrac{40}{5}$

$\implies\sf x=8cm$

$\large\bigstar\: \large{\underline{\sf{\purple{Length\:of\:parallel\:sides}}}}\: {\bigstar}$

• Length of the first parallel side = 2x = 16 cm

• Length of the second parallel side = 3x = 24cm

______________________________________

Answer 2

Answer:

Given :-

• Parallel sides of trapezium are in ratio 2:3
• Distance between them = 16 cm
• Area of trapezium = 320 cm²

To Find :-

Parallel Sides

Solution :-

At, first let's assume the parallel sides as 2x and 3x. Now, After that we will use the formula of finding area of trapezium which is given by

$\large \sf \: Area = \dfrac{1}{2} (a + b) \: h$

½ = 0.5

a and b are parallel sides of trapezium

H is the height.

We also write height as distance

$\sf \: 320 = \dfrac{1}{2} \bigg(2x + 3x \bigg) \times 16$

$\sf \: 320 \times 2 = 1 \times 5x \times 16$

$\sf \: 640 = 1 \times 5x \times 16$

$\sf \: 640 = 5x \times 16$

$\sf \: \dfrac{640}{16} = 5x$

$\sf \: 40 = 5x$

$\sf \: x \: = \dfrac{40}{5}$

$\textsf{x = 8 }$

Hence :-

$\dag {\textsf {\underline{Parallel sides are}}} { \textbf{ \underline {16 and 24 cm }}}$

Know More :-

• Area of rhombus = ½ × D1 × D2

• Area of rectangle = Length × Breadth

• Area of triangle = √s(s-a)(s-b)(s-c)

• Area of Parallelogram = Length×Base