Question

the sides of a triangle are in the ratio of 3:4:5. If its perimeter is 36cm, then what is its area?
a) 32cm²
b) 54cm²
c) 67cm²
d) 72cm²



Explain it plz plzzzz ..​

Answer 1

Answer:

(b) 54 cm²

Step-by-step explanation:

Given :

• Sides of the triangle are in the ratio 3:4:5

• Perimeter of the triangle is equal to 36 cm

To find :

• Area of the given triangle

So according to the question,

3x+4x+5x = 36

12x = 36

x = 36/12

x = 3

Side A = 3x = 3×3 = 9

Side B = 4x = 4×3 = 12

Side C = 5x = 5×3 = 15

$area = \sqrt{s(s - a)(s - b)(s - c)}$

Semi-Perimeter = s = 36/2

Semi-Perimeter = s = 18 cm

$area = \sqrt{18(18 - 9)(18- 12)(18 - 15)}$

$area = \sqrt{18 \times 9 \times 6 \times 3}$

$area = \sqrt{2916}$

Area = 54 cm²

Hence option (b) is correct and the area is equal to 54 cm²

Answer 2

Let, the sides of a triangle are 3x, 4x and 5x.

It is Given that :

Its perimeter is 36 cm. [Given]

So, Sum of all sides of triangle = 36 cm.

Substituting the values, we get,

➮ 3x + 4x + 5x = 36

➮ 12x = 36

➮ x = 36/12

➮ x = 3.

Therefore, We get the value of, x = 3 cm.

Hence,

3x = 3 × 3 = 9 cm

4x = 4 × 3 = 12 cm

5x = 5 × 3 = 15 cm

Now,

We know that, it is an right angled triangle because the sum of squares of two smaller sides is equal to the square of larger sides.

9² + 12² = 15²

15² = 225

Here, the length of hypotenuse is 15 cm.

We know that,

Area of right angled triangle = 1/2 × base × height

Substituting the values in the above formula, we get,

➮ 1/2 × 9 × 12

➮ 9 × 6

➮ 54.

$\therefore$ Area of triangle = 54 cm².

$\therefore$ (b) 54 cm²