The length of the sides of the triangle are in the ratio 3:4:5 and it’s perimeter is 144 cm find its area and height corresponding to the longest side

3:4:5 is one of Pythagorean’s triplets, meaning this is a right triangle.

144 = 3x + 4x + 5x (combine like terms)
144 = 12x (divide both sides by 12)
x = 12
To find the side lengths, multiply 3, 4 and 5 by 12. This means the triangle has sides of 36, 48 and 60 centimetres.

Because this is a right triangle, two of the sides are the base and the height. The hypotenuse (longest side) is not the base nor the height because it is not directly adjacent to the right angle. In this case, the hypotenuse is 60 cm.
A = bh/2
A = (36 cm)(48 cm)/2
A = 864 cm^2
Therefore the area is 864 cm^2.

I’m not sure what is meant by the “height corresponding to the longest side”, sorry.

Hope this helps!