Question

The area of trapezium is 1000 cm2& its height is 20 cm. If one of parallel side is 19 cm shorter than the other, the length of 2 parallel sides are ______________ & ___________​

Answer 1

Question:-

The area of trapezium is 1000 cm2& its height is 20 cm. If one of parallel side is 19 cm shorter than the other, the length of 2 parallel sides are ______________ & ___________

Answer:-

• The parallel sides are 59.5 cm and 40.5 cm.

To find:-

• Parallel sides of trapezium

Solution:-

• Area of trapezium = 1000 cm²
• Height of trapezium = 20 cm

Let,

• Parallel side (a) = x cm
• Parallel side (b) = x – 19 cm

As we know,

$\large{ \boxed{ \mathfrak{area = \frac{a + b}{2} \times h}}}$

Where,

• a and b = parallel sides
• h = height of trapezium

According to question,

$\large{ \tt : \implies \: \: \: \: \: \: \: \frac{(x + x - 19)}{2} \times 20 = 1000}$

$\large{ \tt : \implies \: \: \: \: \: \: \: \frac{(2x - 19)}{2} = \frac{1000}{20} }$

$\large{ \tt : \implies \: \: \: \: \: \: \: 2x - 19 = 50 \times 2}$

$\large{ \tt : \implies \: \: \: \: \: \: \: 2x = 100 + 19}$

$\large{ \tt : \implies \: \: \: \: \: \: \: x = \frac{119}{2} }$

$\large{ \tt : \implies \: \: \: \: \: \: \: x = 59.5}$

• The value of x is 59.5 cm

Now,

• parallel side (a) = 59.5 cm
• parallel side (b) = 40.5 cm

Hence,

• The parallel sides are 59.5 cm and 40.5 cm.