Triangles A B C and D E F are similar triangles.

Question

Two similar triangles.Short description, Two similar triangles.,Long description,
Triangle A B C and triangle D E F are similar.

Side A B is labeled 9 and three-fourths cm and is similar to side D E that is labeled 3 and one-fourth cm.
Side B C is labeled 18 and three-fourths cm and is similar to side E F that is labeled n.
Side C A is labeled 27 and three-fourths cm and is similar to side F D that is labeled 9 and one-fourth cm.

Question
What is the length of side n?

Answer 1

To find the length of side n, we can set up a proportion using the corresponding sides of the similar triangles:

AB/DE = BC/EF = CA/FD

Substituting the given values:

9 and 3/4 cm / 3 and 1/4 cm = 18 and 3/4 cm / n = 27 and 3/4 cm / 9 and 1/4 cm

To simplify the first ratio, we can convert the mixed numbers to improper fractions:

39/4 cm / 13/4 cm = 18 and 3/4 cm / n = 111/4 cm / 37/4 cm

Now we can set up the proportion:

(39/4 cm / 13/4 cm) = (18 and 3/4 cm / n) = (111/4 cm / 37/4 cm)

Cross-multiplying gives us:

(39/4 cm) * n = (13/4 cm) * (18 and 3/4 cm)
(18 and 3/4 cm) * (37/4 cm) = (13/4 cm) * (111/4 cm)

Now we can simplify the equation:

39n/4 = (243/4) + (27/4)
(37/4) * n = (351/4) + (81/4)

Combining like terms:

39n/4 = 324/4 + 81/4
(37/4) * n = (405/4)

Now, we can solve for n by multiplying both sides by 4/37:

n = (405/4) * (4/37)
n = (405/37)

Therefore, the length of side n is 405/37 cm.