Question

The area of triangle with given two sides 18 cm and 10 cm respectively and perimeter equal

to 42 cm is:

a. 20√11 cm2

b. 19√11 cm2

c. 22√11 cm2

d. 21√11 cm2​

Answer 1

✬ 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.

Answer 2

Step-by-step explanation:

Area of triangle

s(s−a)(9−b)(s−0)

Here, s is the semi- perimeter,

and a,b,c are the sides of the triangle

Given a=18 cm, b=10 cm

and perimeter =42 cm

semi- perimeters=

2

perimeter

=

2

42

s=21cm.

Area of triangle

∴c=42−(18+10)cm =14 cm

∴ Area of triangle=

21.(21−18)(21−10)(21−14)

=

21.3.7.11

cm

2

=

3×7×3×7×11

cm

2

=

(3×7)

2

×11

cm

2

=21

11

cm

2

∴ Thus, the required area of the triangle is

21

11

cm

2