Answer:
m = 8 is the missing variable.
Step-by-step explanation:
Given:
Let Name the Triangle First as shown in figure.
∴ Δ AOB ~ Δ BOD
AO = 15
CO = 10
BO = m +4
DO = m
To Find:
m = ?
Solution:
If two triangles are similar then their corresponding sides are proportional, and corresponding angles are equal.
∴ Δ AOB ~ Δ BOD
∴ [tex]\frac{AO}{CO}= \frac{BO}{DO}= \frac{AB}{CD}[/tex] {corresponding sides of similar triangle are in proportion}
∴ [tex]\frac{AO}{CO}= \frac{BO}{DO}[/tex]
Substituting the above given values in it we get
∴ [tex]\frac{15}{10} =\frac{m+4}{m} \\15m=10m+40\\15m-10m=40\\5m=40\\m=\frac{40}{5}\\m= 8[/tex]
∴ BO = m +4 = 8 + 4 = 12
∴ DO = m = 8
