Question

One triangle has side lenghts of 6,8,10. A similar triangle has a perimeter of 60. What are the lengths of the similar triangle?

Answer 1

Answer:

Lengths of second triangle are 15,20,25

Step-by-step explanation:

Given:

One triangle side lengths = 6 , 8 ,10

Similar triangle perimeter =60

To Find:

Lengths of similar triangle = ?

Solution:

A similar triangle is a one in which there is a particular increase in lengths of the sides by a common ratio. This ratio is same for all the sides and by these the similar triangle is formed.

As Lengths are increased by a common ratio so the perimeter of the triangles which are similar will also increase by that

So for this problem if we find out the perimeter increase then we can find out sides

Now For 1st triangle whose sides are given

Lets its perimeter is perimeter 1

Now

Perimeter 1 =sum of length of all sides

                    = 6 + 8 +10

                    = 24

Now

Ratio = Perimeter of second triangle / Perimeter 1

         = 60 / 24

         = 2.5

So perimeter is increased by a factor of 2.5

We can find the length by multiplying each length of triangle 1 with this 2.5

Now Length of first side =  6*2.5

                                         = 15

Length of second side = 8 * 2.5

                                       =20

Length of third side = 10 * 2.5

                                  = 25

Lengths of second triangle are 15,20,25