Triangle A has sides of lengths #2 ,3 #, and #4 #. Triangle B is similar to triangle A and has a side of length #5 #. What are the possible lengths of the other two sides of triangle B?

Question

Triangle A has sides of lengths #2  ,3  #, and #4  #. Triangle B is similar to triangle A and has a side of length #5   #. What are the possible lengths of the other two sides of triangle B?

Aurora Ayala · Accepted Answer

Triangle #1:" " 5, 15/2, 10#
Triangle #2:" " 10/3, 5, 20/3#
Triangle #3:" " 5/2, 15/4, 5# Given : triangle A: sides 2, 3, 4, use ratio and proportion to solve for the possibles sides For example: Let the other sides of triangle B represented by x, y,z If #x=5# find y #y/3=x/2# #y/3=5/2# #y=15/2# solve for z: #z/4=x/2# #z/4=5/2# #z=20/2=10# that completes triangle 1: For triangle #1:" "5, 15/2, 10# use scale factor #=5/2# to obtain the sides #5, 15/2, 10# Triangle #2:" " 10/3, 5, 20/3# use scale factor #=5/3# to obtain the sides #10/3, 5, 20/3# Triangle #3:" " 5/2, 15/4, 5# use scale factor #=5/4# to obtain the sides #5/2, 15/4, 5# God bless...I hope the explanation is useful.

James Atkins · Answer

undefined To find the possible lengths of the other two sides of triangle B, we can use the properties of similar triangles. Since triangle B is similar to triangle A, the corresponding sides are proportional.

The ratio of corresponding sides of similar triangles is constant. Let's denote the length of the unknown side in triangle B as x. We can set up the proportion:

$ \frac{2}{5} = \frac{3}{x} = \frac{4}{\text{other side of triangle B}} $

From the given information, we know that the side lengths of triangle A are 2, 3, and 4. Therefore, the possible lengths of the other two sides of triangle B can be found by solving the proportions:

$ \frac{2}{5} = \frac{3}{x} $

$ 2x = 15 $

$ x = \frac{15}{2} = 7.5 $

Thus, one possible length of the other side of triangle B is 7.5.

Similarly,

$ \frac{2}{5} = \frac{4}{\text{other side of triangle B}} $

$ 4 \times 5 = 2 \times \text{other side of triangle B} $

$ \text{other side of triangle B} = \frac{20}{2} = 10 $

Thus, another possible length of the other side of triangle B is 10. Therefore, the possible lengths of the other two sides of triangle B are 7.5 and 10.