Question

the area of trapezium is 900cmsq2 the distance Between the parellel sides is 24cm . if one of the parellel sides is double the other find the length of the 100 parellel sides​

Answer 1

S O L U T I O N :

Given :

• Area of trapezium = 900 cm²
• Distance between parallel side, (h) = 24 cm

Explanation :

Let the one parallel side be x & other parallel side be 2x

As we know that formula of the area of trapezium:

• Area = 1/2(sum of base) × height

According to the question :

➟ Area of trapezium = 1/2(sum of base) × h

➟ 900 = 1/2( x + 2x) × 24

➟ 900 = 1/2 × 3x × 24

➟ 1800 = 3x × 24

➟ 3x = 1800/24

➟ 3x = 75

➟ x = 75/3

➟ x = 25 cm

Thus,

• The 1st side of trapezium = x = 25cm
• The 2nd side of trapezium = 2x = 2 × 25 = 50cm.

Answer 2

Answer:

Given :-

• The area of trapezium is 900 cm² and the distance between the parallel side is 24 cm.
• One of the parallel sides is double the other.

To Find :-

• What is the length of the parallel sides.

Formula Used :-

✰ Area of trapezium = ½ × (Sum of base) × Height ✰

Solution :-

Let, the first side be x

And, the second side will be 2x

Given :

• Area = 900 cm²
• Height = 24 cm

According to the question by using the formula we get z

⇒ 900 = ½ × (x + 2x) × 24

⇒ 900 = ½ × 3x × 24

⇒ 900 × 2 = 3x × 24

⇒ 1800 = 3x × 24

⇒ 1800 ÷ 24 = 3x

⇒ 75 = 3x

⇒ 75 ÷ 3 = x

⇒ 25 = x

➠ x = 25

Hence, the required sides will be,

❑ First side = x = 25 cm

❑ Second side = 2x = 2(25) = 50 cm

∴ The length of two sides are 25 cm and 50 cm respectively.

Let's Verify :-

↦ 900 = ½ × (x + 2x) × 24

Put x = 25

↦ 900 = ½ × 25 + 2(25) × 24

↦ 900 = ½ × 25 + 50 × 24

↦ 900 = ½ × 75 × 24

↦ 900 = ½ × 1800

↦ 900 = 900

➥ LHS = RHS

Hence, Verified ✔