Question

Assertion: The sides of a triangle are in the ratio of 3: 4: 5 and its perimeter is 144cm. The area of the triangle is 864cm²

Reason: Perimeter of a triangle = a + b + c, where a,b,c are sides of a triangle.​

Answer 1

Answer: Below

Step-by-step explanation:  The three sides of the triangle are in the ratio of 3:4:5.  There is some factor, x, for which we can add the three sides to arrive at the perimeter of the triangle:

3x + 4x + 5x = 144 cm

12x = 144 cm

x = 12 cm

The three sides are 36, 48 and 60 cm.  We know that a 3:4:5 triangle has a right angle.  We also know that if we square and then add the two sides adjacent to the right angle, that it will be equal to the square of the hypothenuse.   We find that 36^2 + 48^2 does indeed equal 60^2 (both are 3600).  The 36 and 48 cm sides are therefore the base and height of this triangle.  Area is (1/2)bh, so A = (1/2)*(36)*(48).  Area = 864cm^2