Triangle A has sides of lengths #18 #, #24 #, and #12 #. Triangle B is similar to triangle A and has a side of length #7 #. 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 7, 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"# Name the 3 sides of triangle B- a , b and c to correspond with the sides- 18 , 24 and 12 in triangle A.
#color(blue)"-------------------------------------------------------"#
If side a = 7 then ratio of corresponding sides#=7/18# and side b
#=24xx7/18=28/3," side c " =12xx7/18=14/3# The 3 sides of B would be
#(7,color(red)(28/3),color(red)(14/3))#
#color(blue)"--------------------------------------------------------------"# If side b = 7 then ratio of corresponding sides
#=7/24# and side a
#=18xx7/24=21/4," side c " =12xx7/24=7/2# The 3 sides of B would be
#(color(red)(21/4),7,color(red)(7/2))#
#color(blue)"-------------------------------------------------------------------"# If side c = 7 then ratio of corresponding sides
#=7/12# and side a
#=18xx7/12=21/2," side b " =24xx7/12=14# The 3 sides of B would be
#(color(red)(21/2),color(red)(14),7)#
#color(blue)"--------------------------------------------------------------------"#