Question

The lengths of the sides of a triangles are in the ratio 3: 4: 5 and its perimeter is 144cm. Find the area of the triangle and the height corresponding to the greatest side.

Answer 1

Here given that the lengths of triangle are in the ratio

3 : 4 : 5

So, Let the sides be 3x, 4x and 5x respectively.


Given that perimeter = 144 cm

We know that

Perimeter = Sum of all sides

=> 144 = 3x + 4x + 5x

=> 144 = 12x

=> x = 144/12

=> x = 12 cm

So first side = 3x = 3 × 12 = 36 cm

Second side = 4x = 4 × 12 = 48 cm

Third side = 5x = 5 × 12 = 60cm

Now, If you see carefully, you will find that,


60² = 36² + 48²

Since the square of longest side = sum of square if other two side

we can say that the given ∆ is a right angled triangle


So either 36 or 48 is base or height

area = 1/2 × b × h

So area = 1/2 × 36 × 48

=> area = 864 cm²

So height = either 36 or 48 but since, the ratios are 3 : 4 : 5

=> height = 4x = 48cm


Hope it helps dear friend ☺️

Answer 2

HEY MATE HERE IS YOUR ANSWER IN ATTACHMENT

Area = 864 cm ^2

Hope it will help you