Question

∆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 how many units? If the height of ∆ABC, with respect to its longest side being the base, is 8 units, the area of ∆XYZ is how many square units?

Answer 1

Answer:135 units

600 square units

Answer 2

Let the longest side of ΔABC is c = 24 and the longest side of ΔXYZ is z = 60
The ratio of any pair of corresponding sides of these triangles is the same:
z/c = 60/24 = 2.5
x = 10 · 2.5 = 25
y = 20 · 2.5 = 50
The perimeter of ΔXYZ : 25 + 50 + 60 = 135 units
hc = 8
hz = 8 · 2.5 = 20
The area of ΔXYZ : 60 · 20 / 2 = 600 square units