Question

the area of the trapezium is 92.4cm² and its height is 5.6cm if one of the parallel sides is longer than the other by 3cm find the lengths of two sides​

Answer 1

Given -

The area of the trapezium is 92.4cm² and its height is 5.6cm if one of the parallel sides is longer than the other by 3cm.

To find -

• Length of two sides of trapezium

Solution -

• Area of the trapezium = 92.4cm²
• Height of the trapezium = 5.6cm

★ If one of the parallel sides is longer than the other by 3cm.

Let the parallel sides of trapezium be x and (x + 3)

• According to the formula of area of the trapezium

→ ½ × sum of parallel sides × height

→ ½ × (a + b) × h = 92.4cm²

→ ½ × (x + x + 3) × 5.6 = 92.4

→ ½ × (2x + 3) × 5.6 = 92.4

→ (2x + 3) × 2.8 = 92.4

→ 2x + 3 = 92.4/2.8

→ 2x + 3 = 33

→ 2x = 33 - 3

→ 2x = 30

→ x = 30/2

→ x = 15 cm

•°• First parallel side = x = 15cm

•°• Second parallel side = x + 3 = 18cm

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Answer 2

Answer:

Given :-

• The area of the trapezium is 92.4 cm² and its height is 5.6 m. If one of the parallel sides is longer than the other by 3 cm.

To Find :-

• What is the length of two sides.

Formula Used :-

✪ Area of trapezium = 1/2 × Sum of parallel sides × Height ✪

Solution :-

Let, the first side be x

And, the second side will be x + 3

Given :

• Area = 92.4 cm²
• Height = 5.6 m

According to the question by using the formula we get,

⇒ 92.4 = 1/2 × x + x + 3 × 5.6

⇒ 92.4 = 1/2 × 2x + 3 × 5.6

⇒ 92.4 = 1/2 × 5.6 × 2x + 3

⇒ 92.4 = 2.8 × 2x + 3

⇒ 92.4/2.8 = 2x + 3

⇒ 33 = 2x + 3

⇒ 33 - 3 = 2x

⇒ 30 = 2x

⇒ 30/2 = x

⇒ 15 = x

➠ x = 15

Hence, the required parallel sides are,

✧ First side = x = 15 cm

✧ Second side = x + 3 = 15 + 3 = 18 cm

∴ The length of two sides are 15 cm and 18 cm.