Q12 The sides of a triangle are in the
ratio of 3:4:5. If its perimeter is 36
cm, then what is its area?
Answers
Answer:
Let the sides of a triangle in the ratio be 3x,4x,5x
Perimeter of triangle = a + b + c
=> 36 = 3x + 4x + 5x
,=>36 = 12x
=>x =36/12
= 3
Thus, sides of the triangle are 3x =3 * 3 =9 cm
4x =4 * 3= 12cm
5x =5 * 3=15cm
The value of x is 3. The length of sides are 9, 12, 15.
It is an right angled triangle because the sum of squares of two smaller sides is equal to the square of larger sides.
Here, the length of hypotenuse is 15 cm.
The area of triangle
0.5 * b * h
= 0.5* 9 * 12
= 54cm
Therefore the area of triangle is 54 cm².