Triangle A has sides of lengths #12 #, #9 #, and #6 #. Triangle B is similar to triangle A and has a side of length #24 #. What are the possible lengths of the other two sides of triangle B?

Question

Triangle A has sides of lengths #12    #, #9    #, and #6     #. Triangle B is similar to triangle A and has a side of length #24     #. What are the possible lengths of the other two sides of triangle B?

Sophia Alfred · Accepted Answer

The other two lengths are #18# and #12#

Similarity in simple words means that two objects have the same shape But, have different sizes.

We can find the other two sides using the proportionality of the first corresponding sides

Consider the diagrams

Use the proportionality

#:.color(blue)(24/12=x/9=y/6#

Solve for #x/9#

#rarr24/12=x/9#

#rarr2=x/9#

#color(green)(rArrx=9*2=18#

Solve for #y/6#

#rarr24/12=y/6#

#rarr2=y/6#

#color(green)(rArry=6*2=12#

Sophia Alfred · Answer

undefined To find the lengths of the other two sides of triangle B, we use the property of similar triangles, which states that corresponding sides of similar triangles are in proportion.

Given that triangle B is similar to triangle A, the ratio of the corresponding sides of triangle B to triangle A is constant.

The ratio of the side lengths of triangle B to triangle A is 24/12 = 2.

Using this ratio, we can find the lengths of the other two sides of triangle B:

- The length of the side corresponding to 9 in triangle A is 9 * 2 = 18.
- The length of the side corresponding to 6 in triangle A is 6 * 2 = 12.

Therefore, the possible lengths of the other two sides of triangle B are 18 and 12.