Question

4. Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is
42cm.
5. Sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540cm. Find its area.
qual sides is 12 cm Find
2am
of 1​

Answer 1

Ques :- Find the area of a triangle, two sides of which are 18cm and 10cm and the perimeter is 42 cm :

Answer :-

Given that,

Two sides of triangle are 18 cm and 10 cm.

Perimeter of triangle is 42 cm

Let, third side of triangle be x .

So,

$\longrightarrow$ Perimeter = 18 + 10 + x

$\longrightarrow$ 42 = 28 + x

$\longrightarrow$ 42 - 28 = x

$\longrightarrow$ x = 14

Third side of triangle is 14 cm.

Now,

s = 42/2

s = 21

Semi-perimeter is 21 cm.

Area of traingle :

$\longrightarrow$ √21 × (21 -18)(21 -14)(21 - 10)

$\longrightarrow$ √21 × 3 × 7 × 11

$\longrightarrow$ √3 × 7 × 3 × 7 × 11

$\longrightarrow$ 3 × 7 √11

$\longrightarrow$ 21 × √11

• Put √11 = 3.316

$\longrightarrow$ 21 ×3.316

$\longrightarrow \pink{\boxed{\bold{69.639}}\bigstar}$

Area of triangle is 69.636 cm².

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Ques :- Sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540cm. Find its area.

Answer :-

Given that,

Sides of triangle are in ratio 12:17:25.

Perimeter of triangle is 540 cm.

Let, Sides of triangle be 12x, 17x and 25x.

So,

$\longrightarrow$ Perimeter = 12x + 17x + 25x

$\longrightarrow$ 540 = 54x

$\longrightarrow$ x = 540/54

$\longrightarrow$ x = 10

Sides:

12x = 12 × 10 = 120 cm

17x = 17 × 10 = 170 cm.

25x = 25 × 10 = 250 cm.

Now,

s = 540/2

s = 270

Semi-perimeter is 270 cm.

Area of traingle :

$\longrightarrow$ √270 × (270 - 120)(270 -170)(270 - 250)

$\longrightarrow$ √270 × 150 × 100 × 20

$\longrightarrow$ √2×5×3×3×3×2×5×5×3×2×2×5×5×2×2×5

$\longrightarrow$ 2 × 2 × 2 × 5 × 5 × 5 × 3 × 3

$\longrightarrow \purple{\boxed{\bold{9000}}\bigstar}$

Area of traingle is 9000 cm².

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Formulas used:-

• Perimeter of triangle = Sum of all sides

• Heron's formula that is

Area of traingle = √s(s - a)(s - b)(s - c)

where,

• s is semi-perimeter of triangle.
• a, b and c are sides of triangle.

• Semi-perimeter = Perimeter of triangle/2