Question

The area of a trapezium with of of the parallel sides four times the other side is 240cm?
If it's length is 12cm, then the length of the longer of the two parallel sides? ​

Answer 1

Step-by-step explanation:

Given:-

• The area of the trapezium = 240cm².

• The length of a parallel side is four times the other parallel side.

• The distance between the parallel sides = 12cm.

To Find:-

• The length of the longer parallel side.

Solution:-

Area of the trapezium = 240cm²

Height of trapezium = 12cm

Let, the length of a parallel side be x

And the other parallel side = 4x

$\boxed{ \bull \: \sf Area \: of \: a \: trapezium = \frac{1}{2} \times (sum \: of \: parallel \: sides) \times Height }$

$\sf \implies \dfrac{1}{2} \times (x + 4x) \times 12 = 240$

$\sf \implies \dfrac{1}{2} \times 5x \times 12 = 240$

$\sf \implies 5x \times 6 = 240$

$\sf \implies 30x = 240$

$\sf \implies x = \dfrac{240}{30}$

$\sf \implies x = 8$

Length of a parallel side = 8cm.

Length of the other parallel side = 4x = 4 × 8 = 32cm.

$\underline{\boxed{\sf \therefore Length\: of \: the \: longer \: parallel\: side = 32cm}}$

Answer 2

{* I want to inform that I haven't copied from anyone. It's my own answer}

===================================

Correct Question:-

The area of a trapezium with once of the parallel sides four times the other side is 240cm² ? If it's height length is 12cm, then the length of the longer of the two parallel sides?

Answer :-

${ \large{\sf{\bigstar{ \: Given : }}}}$

• One of the parallel side is four times of the other side.
• Area is 240 cm²
• Length of the height is 12 cm.

${ \large{\sf{\bigstar{ \: To \: find : }}}}$

• Length of the longer of the two parallel sides.

${ \large{\sf{\bigstar{ \:Assume \: that : }}}}$

• One of the parallel side of the Trapezium be x.
• Then other one will be 4x because one of the parallel side is four times of the other side.

${\sf{\bigstar{ \:So, according \: to \: the \: question }}}$

${ \bold{\boxed{\color{red}{\sf{Area = \frac{1}{2} (Sum \: of \: parallel \: side) × Height}}}}}$

${ \bold{\boxed{{\sf{Area = \frac{1}{2} (AB + CD ) × Height}}}}}$

$\: \: \: \: \: \: \: {\sf{\implies{ 240 = \frac{1}{2} \times (x + 4x) \times 12}}}$

$\: \: \: \: \: \: \: {\sf{\implies{240 = \frac{1}{2} \times (5x) \times 12}}}$

$\: \: \: \: \: \: \: {\sf{\implies{240 = \frac{1}{ \cancel{2}^{1} } \times (5x) \times \cancel{12}^{6} }}}$

$\: \: \: \: \: \: \: {\sf{\implies{240 = 1 \times 5x \times 6}}}$

$\: \: \: \: \: \: \: {\sf{\implies{240 = 6 \times 5x}}}$

$\: \: \: \: \: \: \: {\sf{\implies{ \frac{240}{6} = 5x}}}$

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

$\: \: \: \: \: \: \: {\sf{\implies{x = \frac{40}{5} }}}$

$\: \: \: \: \: \: \: { \large{ \boxed{\sf{\implies{x = 8}}}}}$

${\sf{\bigstar{ \:So, Length \: of \: the \: both \: parallel \: side \: is }}}$

${ \large{\mathtt{{ \bold{\implies}{{x = {\boxed{\color{green}{8 \: cm}}}}}}}}}$

${ \large{\mathtt{{ \bold{\implies}{{4x = 4 \times 8 = {\boxed{\color{green}{32 \: cm}}}}}}}}}$

So, length of the longer side is 32 cm.