Triangle A has sides of lengths #15 #, #12 #, and #18 #. Triangle B is similar to triangle A and has a side of length #3 #. What are the possible lengths of the other two sides of triangle B?

Question

Triangle A has sides of lengths #15    #, #12    #, and #18     #. Triangle B is similar to triangle A and has a side of length #3     #. What are the possible lengths of the other two sides of triangle B?

Autumn Armstrong · Accepted Answer

#(3,12/5,18/5),(15/4,3,9/2),(5/2,2,3)# Since triangle B has 3 sides, anyone of them could be of length 3 and so there are 3 different possibilities. Since the triangles are similar then the ratios of corresponding sides are equal. Name the 3 sides of triangle B , a, b and c corresponding to the sides 15 , 12 and 18 in triangle A. #"----------------------------------------------------"# If side a = 3 then the ratio of corresponding sides#=3/15=1/5# hence b#=12xx1/5=12/5" and " c=18xx1/5=18/5# The 3 sides of B#=(3,12/5,18/5)# #"---------------------------------------------------"# If side b = 3 then the ratio of corresponding sides#=3/12=1/4# hence a#=15xx1/4=15/4" and "c=18xx1/4=9/2# The 3 sides of B#=(15/4,3,9/2)# #"---------------------------------------------------"# If side c = 3 then the ratio of corresponding sides#=3/18=1/6# hence a#=15xx1/6=5/2" and "b=12xx1/6=2# The 3 sides of B #=(5/2,2,3)# #"------------------------------------------------------"#

Evelyn Arboleda · Answer

undefined Since triangle B is similar to triangle A, their corresponding sides are proportional. Let's denote the lengths of the sides of triangle B as $ x $ and $ y $.

Using the property of similarity, we can set up the following proportion:

$$\frac{x}{15} = \frac{3}{12} = \frac{y}{18}$$

Solving for $ x $ and $ y $ gives:

$$x = \frac{3}{12} \times 15 = \frac{15}{4} = 3.75$$

$$y = \frac{3}{12} \times 18 = \frac{9}{2} = 4.5$$

So, the possible lengths of the other two sides of triangle B are $3.75$ and $4.5$.