Question

In the diagram below, TO = 10, GO = 6, and CT = 24. If points D, O, and G are midpoints, what is the perimeter of ∆CAT?

Answer 1

EXPLANATION

IF O is a midpoint of TA, then TO is a half of TA and

TA = 2*TO

TA= 2* 10 = 20

So, TA = 20

Then, CT = 24

Now, we need to find the CA length.

If GO=6, The sides of the triangle formed by connecting the midpoints are half the sides of the original triangle.

So, in this case, is side GO=6 then side CA is equal to 12.

CA=12

So, the perimeter is equal to the sum of the sides TA+CT+CA

Perimeter = TA+CT+CA = 20 + 24 + 12 = 56

The perimeter of △CAT is equal to 56