Please help! This is due tomorrow. Suppose �£ABC ~ �£GHI with scale factor 3:5, AB = 9, BC = 18, and AC = 21. Find the perimeter of �£GHI.
Oops that latin word is suppose to be a Triangle in this question. Sorry.
To find the perimeter of ∆GHI, we need to know the lengths of its sides. Since ∆ABC and ∆GHI are similar triangles with a scale factor of 3:5, their corresponding sides are proportional.
Given that AB = 9, BC = 18, and AC = 21, we can use these lengths to find the lengths of the corresponding sides of ∆GHI.
First, let's determine the ratio of the corresponding sides.
For ∆ABC, the ratio of corresponding sides can be written as: AB:BC:AC = 9:18:21.
Using this ratio, we can find the lengths of GH, HI, and GI.
GH = (3/5) * AB = (3/5) * 9 = 27/5 = 5.4
HI = (3/5) * BC = (3/5) * 18 = 54/5 = 10.8
GI = (3/5) * AC = (3/5) * 21 = 63/5 = 12.6
Now that we have the lengths of all three sides of ∆GHI, we can calculate the perimeter by adding up the lengths of the sides.
Perimeter of ∆GHI = GH + HI + GI
= 5.4 + 10.8 + 12.6
= 28.8
Therefore, the perimeter of ∆GHI is 28.8 units.