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?
1 Answer
Explanation:
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)"----------------------------------------------------------------"#
