Question

The ratio of the altitudes of a triangle is 2 : 3 : 4. find the sides of the triangle, if its perimeter is 91 cm.

Answer 1

Common multiple of ratio of altitudes is y and sides of the triangle are a,b and c.....
I've equated areas of the triangle considering different altitudes and sides each time...
Hope it's helpful .

Answer 2

Answer: The sides of the triangle are 42 cm , 28 cm and 21 cm.

Step-by-step explanation:

Area of a triangle = $\frac{1}{2}$ × (base) × (altitude)

Area of a given triangle is fixed. Therefore, product of altitude and base is fixed.

Ratio of altitude = 2 : 3 : 4

∴ Ratio of base = $\frac{1}{2} : \frac{1}{3} : \frac{1}{4}$

Let the sides (bases) be x/2 , x/3 and x/4 cm

Perimeter of triangle = Sum of the three sides

$91 = \frac{x}{2} + \frac{x}{3} + \frac{x}{4}$

$91 = \frac{13x}{12}$

$x = 84$

Sides of triangle :

x/2 cm = 42 cm

x/3 cm = 28 cm

x/4 cm = 21 cm

#SPJ3