Question

As shown in the diagram of the right triangles below, Triangle: ABC ~ Triangle: DEF, AB = 7x, BC = 4, DE = 7, EF = x. What is thr perimeter of Triangle: DEF to the nearest hundredth?​

Answer 1

since triangles are similar

4/x = 7x/7

=》 4/x = x

=》x^2 = 4

=》 x = 2

for right triangles a^2 = b^2+c^2

DF^2 = 7^2+2^2 = 53

=》 DF = 7.28

perimeter of DEF = 7 +2+7.28 = 16.28