Question

find the area of a triangle whose sodes are5:12:13and its perimetre is 60 cm.
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Answer 1

Answer:

#According to question

first side = 5x

second side = 12x

third side = 13x

sum of all sides = perimeter = 60

5x + 12x + 13x = 60

30x = 60

x = 2

thus

first side = 5 x 2 = 10cm

second side = 12 x 2 = 24cm

third side = 13 x 2 = 26cm

as we can see that

26² = 24² + 10²

676 = 576 + 100 = 676

so Pythagoras theorem is applied here

this conclude that given triangle is right angle triangle.

area of triangle = 1/ 2 x base x height

area of triangle = 1/ 2 x base x heightarea = 1/2 x 10 x 24 = 12 x 10

area = 120

hope this will help you____

Answer 2

Answer:

120 cm²

Step-by-step explanation:

Let the sides of the triangle be 5x, 12x and 13x.

Given : Perimeter of triangle = 60 cm

Therefore,

→ 5x + 12x + 13x = 60 cm

→ 30x = 60

→ x = 60/30

→ x = 2

Now, the sides of triangle are :

First side, a = 5x = 5(2) = 10 cm

Second side, b = 12x = 12(2) = 24 cm

Third side, c = 13x = 13(2) = 26 cm

Now,

Area of triangle can be deduced by using Heron's formula.

s = (a + b + c)/2 = (10 + 24 + 26)/2

s = 60/2 = 30

Now,

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

Putting known values, we get

→ √30(30 - 10)(30 - 24)(30 - 26)

→ √30(20)(6)(4)

→ √6 × 6 × 10 × 10 × 2 × 2

→ 6 × 2 × 10

→ 120 cm²

Hence, the area of triangle is 120 cm².