∆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.

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 
 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.

surjithayer · Answer

$$area~of~\triangle~ABC=\frac{ 1 }{ 2 }\times 24\times 8=96~squareunits.$$
scale factor=60/24=5/2
$$area~of~\triangle XYZ=(\frac{5}{2})^2 \times 96=600~ units ^2$$