The perimeter of a triangle is 60 cm. and the lengths of the sides are in the ratio of 4:5:6. How do you find the length of each side?

Question

Savannah Anderson · Accepted Answer

If we name the three sides as #a,b,c#, than the proportion says:

#a:4=b:5=c:6#.

Using the property of the proportions (that is using before the compound and than the invertion of terms):

#a:b=c:drArr(a+c):(b+d)=a:b# #(or c:d)#,

than:

#(a+b+c):(4+5+6)=a:4rArr#

#60:15=a:4rArra=(60*4)/15=16#

or:

#60:15=b:5rArrb=(60*5)/15=20#

or:

#60:15=c:6rArrc=(60*6)/15=24#.

Genesis Allen · Answer

undefined To find the length of each side of the triangle, we can use the fact that the perimeter is equal to the sum of all three sides.

Let's denote the lengths of the sides as 4x, 5x, and 6x, where x is a common factor.

According to the given ratio, the sum of these three sides is equal to 60 cm.

So, we have the equation: 4x + 5x + 6x = 60

Combining like terms, we get: 15x = 60

Dividing both sides by 15, we find: x = 4

Now, we can substitute this value back into the lengths of the sides:

Side 1: 4x = 4 * 4 = 16 cm 
Side 2: 5x = 5 * 4 = 20 cm 
Side 3: 6x = 6 * 4 = 24 cm

Therefore, the lengths of the sides are 16 cm, 20 cm, and 24 cm.