Question

The area of a trapezium is 850 sq. cm. One of the parallel sides is 64 cm and the perpendicular
distance between the parallel sides is 17 cm. Find the length of other parallel side. ​

Answer 1

Given :

Area of trapezium = 850 sq.m

Length of one of the parallel sides = 64 cm

Perpendicular distance between the parallel sides = 17 cm

To Find :

The length of the other parallel side

Solution :

Area of a trapezium is given by ,

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

Here ,

a and b are length of parallel sides

h is distance between the parallel sides

We have ,

a = 64 cm

A = 850 sq.m

d = 17 cm

Substituting the values ;

$\\ : \implies \sf \: 850 = \frac{1}{2} \times (64 + b) \times 17$

$\\ : \implies \sf \: 850 \times 2 = (64 +b) \times 17$

$\\ : \implies \sf \: 1700 = (64 + b) \times 17$

$\\ : \implies \sf \: \frac{1700}{17} = 64 + b$

$\\ : \implies \sf \: 64 + b = 100$

$\\ : \implies \sf \: b = 100 - 64$

$\\ : \implies {\underline{\boxed{\pink{\mathfrak{b = 36 \: cm}}}}} \: \bigstar$

Hence ,

The length of the other parallel side is 36 cm

Answer 2

Answer:

• Other parallel side of trapezium is 36 cm.

Step-by-step explanation:

Given :-

• Area of trapezium is 850 cm².
• One parallel side is 64 cm.
• Perpendicular distance between the parallel sides is 17 cm.

To find :-

• Length of other parallel side.

Solution :-

Let, Other parallel side of trapezium be x.

We know,

Area of parallelogram = (a + b)/2 × h

Where,

• a and b are parallel sides of trapezium.
• h is height or we can say distance between parallel sides.

Put all values in formula:

⇒850 = (a + b)/2 × h

⇒850 = (65 + x)/2 × 17

⇒850/17 = (65 + x)/2

⇒50 = (65 + x)/2

⇒50 × 2 = 65 + x

⇒100 = 65 + x

⇒100 - 65 = x

⇒x = 36

We take,

Other parallel side be x.

So,

Other parallel side of trapezium is 36 cm.