Determine two triangles

Question

Triangle A is 24 cm wide and 20 cm high.

Triangle B is 14.4 cm wide and similar to triangle A.

 

a) Determine the scale factor needed to reduce triangle A to form triangle B.

 

b) Determine the areas of the triangle A and triangle B.

 

c) How many triangles congruent to triangle B would fit inside triangle A?

 

Answer 1

The width and heights of similar triangles are proportionate.

Hence the width of Triangle A being W_a and that of Triangle B being W_b and also respective heights of Triangle A and triangle B being H_a and H_b, for triangle A and triangle B to be similar triangles W_a/W_b=H_a/H_b =K  or W_a/H_a=W_b/H_b =K, where K is a constant of proportion. Thus, W_a=KW_b, H_a=KH_b K being the scale factor , W_a=KH_a, W_b=KH_b

Given that, W_a=24 cm, H_a=20 cm Hence, K=W_a/W_b=24/20=6/5= 1.2

Also given that, W_b=14.4 cm, Hence H_b=14.4/1.2=12 cm

Area of triangle A = (1/2)*W_a*H_a=(1/2)*24*20=240 sq. cm

Area of triangle B = (1/2)*W_b*H_b=(1/2)*14.4*12=86.4 sq. cm

The number of triangles congruent to triangle B that can fit inside triangle is 2 as 86.4*3=259.2 sq. cm which is > 240 sq cm, area of triangle A but 86.4*2=172.8 sq cm which is < 240 sq cm, area of triangle A.