∆ABC has side lengths of 10 units, 20 units, and 24 units. ∆XYZ is similar to ∆ABC, and the length of its longest side is 60 units. The perimeter of ∆XYZ is units. If the height of ∆ABC, with respect to its longest side being the base, is 8 units, the area of ∆XYZ is square units. NextReset

Accepted Solution

To find the perimeter of triangle XYZ, you will need to find out how many groups of 24 it takes to get 60(both are the longest sides). The answer is 2.5 (You divide to get this). You then multiply the other 2 sides (20 and 10) by 2.5. The other two sides would be 50 and 25. Add 60+50+25 to get a perimeter of 135 units. To find the area, you will use the same factor (2.5) to find the height of triangle XYZ. So, 8 x 2.5= 20 for the height of triangle XYZ. Please see the picture to help further understand this relationship and see the work for finding the area of triangle XYZ.