Question

The area of triangle with given two sides 18cm and 10cm respectively and perimeter equal to 42 cm is:​

Answer 1

Step-by-step explanation:

Given:

Perimeter of triangle is 42 cm.

Measure of two sides of triangle are 18 and 10 cm respectively.

To Find:

What is the area of triangle?

Solution: Let the third side of triangle be x cm. Therefore,

➯ Sum of all sides = Perimeter

➯ 18 + 10 + x = 42

➯ x = 42 – 28

➯ x = 14 cm { Third sides of triangle }

Now, For finding area of ∆ we will use Heron's Formula.

First find the Semi-Perimeter (s)

➬ s = (Sum of all sides / 2)

➬ s = (42/2)

➬ s = 21

★ Formula = √s(s–a) (s–b) (s–c) ★

➛ √21 (21 – 18) (21 – 10) (21 – 14)

➛ √21 (3) (11) (7)

➛ √3 \times× 7 \times× 3 \times× 11 \times× 7

➛ 3 \times× 7 √11

➛ 21√11 cm²

Hence, the area of triangle is 21√11 cm²

Answer 2

Answer:

✬ Area = 21√11 cm² ✬

Step-by-step explanation:

Given:

Perimeter of triangle is 42 cm.

Measure of two sides of triangle are 18 and 10 cm respectively.

To Find:

What is the area of triangle?

Solution: Let the third side of triangle be x cm. Therefore,

➯ Sum of all sides = Perimeter

➯ 18 + 10 + x = 42

➯ x = 42 – 28

➯ x = 14 cm { Third sides of triangle }

Now, For finding area of ∆ we will use Heron's Formula.

First find the Semi-Perimeter (s)

➬ s = (Sum of all sides / 2)

➬ s = (42/2)

➬ s = 21

★ Formula = √s(s–a) (s–b) (s–c) ★

➛ √21 (21 – 18) (21 – 10) (21 – 14)

➛ √21 (3) (11) (7)

➛ √3 \times× 7 \times× 3 \times× 11 \times× 7

➛ 3 \times× 7 √11

➛ 21√11 cm²

Hence, the area of triangle is 21√11 cm². Option (d) is correct.