Triangle A has sides of lengths #28 #, #36 #, and #24 #. Triangle B is similar to triangle A and has a side of length #8 #. What are the possible lengths of the other two sides of triangle B?

Question

Triangle A has sides of lengths #28    #, #36    #, and #24     #. Triangle B is similar to triangle A and has a side of length #8     #. What are the possible lengths of the other two sides of triangle B?

Mason Adams · Accepted Answer

#(8,72/7,48/7),(56/9,8,16/3),(28/3,12,8)#

Anyone of the 3 sides of triangle B could be of length 8, hence there are 3 different possibilities for the sides of B.

Since the triangles are similar then the #color(blue)"ratios of corresponding sides are equal"#

Label the 3 sides of triangle B, a, b and c to correspond with the sides 28, 36 and 24 in triangle A. #color(blue)"-----------------------------------------------------"# If side a = 8 then ratio of corresponding sides #=8/28=2/7#

and side b #=36xx2/7=72/7, " side c" =24xx2/7=48/7#

The 3 sides of B would be #(8,color(red)(72/7),color(red)(48/7))# #color(blue)"-----------------------------------------------------------"# If side b = 8 then ratio of corresponding sides #=8/36=2/9#

and side a #=28xx2/9=56/9 , c=24xx2/9=48/9#

The 3 sides of B would be #(color(red)(56/9),8,color(red)(48/9))# #color(blue)"-----------------------------------------------------------------"# If side c = 8 then ratio of corresponding sides #=8/24=1/3#

and side a #=28xx1/3=28/3 , b=36xx1/3=12#

The 3 sides of B would be #(color(red)(28/3),color(red)(12),8)# #color(blue)"----------------------------------------------------------------"#

Caroline Aucoin · Answer

undefined The possible lengths of the other two sides of triangle B are $ \frac{64}{9} $ and $ \frac{32}{3} $.