Question

The area of a Trapezium is 200cm square and it's height is 8cm. If one of the parallel sides is longer than the other by 6 cm. Find the parallel sides​

Answer 1

Given :

• Area of the trapezium = 200 cm²
• Height of the trapezium = 8 cm
• one of the parallel sides is longer than the other by 6 cm

To Find :

• The parallel sides of the trapezium

Solution :

Let the parallel sides be "a" and "b" . Then the two parallel sides of trapezium are a and a + 6 {given condition}

Area of trapezium is given by ,

$\\ \star \: {\boxed{\purple{\sf{Area_{(trapezium)} = \frac{1}{2} \times (a + b) \times h}}}}$

$\\ \sf{Here}\begin{cases}\sf{a\:and\:b\:are\:parallel\:sides} \\ \\ \sf{h\:is\:height \: of \: trapezium}\end{cases}$

Substituting the values we have ,

$\\ : \implies \sf \: 200 = \frac{1}{2} \times (a + a + 6) \times 8$

$\\ : \implies \sf \: 200 = \frac{1}{2} \times (2a + 6) \times 8$

$\\ : \implies \sf \: 200 = 4 \times (2a + 6)$

$\\ : \implies \sf \: 2a + 6 = \frac{200}{4}$

$\\ : \implies \sf \: 2a + 6 = 50$

$\\ : \implies \sf \: 2a = 50 - 6$

$\\ : \implies \sf \: 2a = 44$

$\\ : \implies \sf \: a = \frac{44}{2}$

$\\ : \implies{\underline{\boxed {\pink{\mathfrak{a =22 \: cm }}}}} \: \bigstar$

$\qquad$━━━━━━━━━━━━━━━━━

Then the other parallel side b is ;

$\\ : \implies \sf \: b = a + 6$

$\\ : \implies \sf \: b = 22 + 6 \: cm$

$\\ : \implies{\underline{\boxed {\pink{\mathfrak{b = 28 \: cm}}}}} \: \bigstar$

Hence ,

• The parallel sides of the given trapezium are 22 cm and 28 cm

Answer 2

Answer:

Given :-

• Area of trapezium = 200 cm ²
• Height = 8 cm
• One parallel sides is 6 cm longer than other

To Find :-

Parallel sides

Solution :-

As we know that

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

Let the parallel side be x and x+6

$\tt \: 200 = \dfrac{1}{2} \times (x + x + 6) \times 8$

$\tt \: 200 = \dfrac{1}{2} \times (2x + 6) \times 8$

$\tt \: 200 = 1 \times 4(2x + 6)$

$\tt \: 200 = 4 \times 2x + 6$

$\tt \: \dfrac{200}{4} = 2x + 6$

$\tt \: 50 = 2x + 6$

$\tt \: 50 - 6 = 2x$

$\tt \: 44 = 2x$

$\tt \: x \: = \dfrac{44}{2}$

$\tt \: x \: = 22$

$\tt \: x + 6 = 22 + 6 = 28$

Hence :-

The parallel sides are 22 and 28