Question

the area of trapezium is 448 cm2 its parallel sides are in the ratio 3:5 and the the perpendicular distance between them is 14cm find the length of each parallel side​

Answer 1

Step-by-step explanation:

area of trapezium = 1/2×(b+a)×h

448cm² = 1/2×(3x+5x)×14

448cm²=1/2×7x×14

448cm²=49x

448/49 = x

Answer 2

Question:-

the area of trapezium is 448 cm² its parallel sides are in the ratio 3:5 and the the perpendicular distance between them is 14cm find the length of each parallel side

Answer:-

• The parallel sides of trapezium are 24 cm and 40 cm.

To find:-

• Parallel sides of trapezium

Solution:-

• Area of trapezium = 448 cm²
• Height of trapezium = 14 cm
• Ratio of parallel sides = 3:5

Put x in the ratio,

• a = 3x
• b = 5x

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,

$\large{ \tt : \implies \: \: \: \: \: \: \: \: \: \: \frac{3x + 5x}{2} \times 14 = 448}$

$\large{ \tt : \implies \: \: \: \: \: \: \: \: \: \: \frac{3x + 5x}{2} = \frac{448}{14} }$

$\large{ \tt : \implies \: \: \: \: \: \: \: \: \: \: 8x = 32 \times 2}$

$\large{ \tt : \implies \: \: \: \: \: \: \: \: \: \: 8x = 64}$

$\large{ \tt : \implies \: \: \: \: \: \: \: \: \: \: x = \frac{64}{8} }$

$\large{ \tt : \implies \: \: \: \: \: \: \: \: \: \: x = 8}$

• The value of x is 8 cm

Now,

• a = 3x = 24 cm
• b = 5x = 40 cm

Hence,

• The parallel sides of trapezium are 24 cm and 40 cm.