Question

The triangles are similar. find the length of each side of the smaller triangle to the nearest 0.01

Answer 1

In the given similar traingles ABC and MNO

From the properties of similar triangle :

The ratio of corresponding sides of similar triangle are always equal

In the triangle ABC and MNO

`(AB)/(MN)=(BC)/(NO)=(CA)/(OM)`

In the given figure, we have : AB = 12, BC = 10, NO = 3

`\begin{gathered} (AB)/(MN)=(BC)/(NO)=(CA)/(OM) \\ (12)/(MN)=(10)/(3)=(CA)/(OM) \\ \text{ simplify the first two and solve for MN} \\ (12)/(MN)=(10)/(3) \\ MN=(3*12)/(10) \\ MN=(36)/(10) \\ MN=3.6\text{ cm} \end{gathered}`

In triangle ABC apply pythagoras for the side AC

`\begin{gathered} \text{ Hypotenuse}^2=Perpendicular^2+Base^2 \\ AC^2=AB^2+BC^2 \\ AC^2=12^2+10^2 \\ AC^2=144\text{ + 100} \\ AC^2=244 \\ AC=\sqrt[]{244} \\ AC=15.62\text{ cm} \end{gathered}`

Now apply the corresponding ratio :

`\begin{gathered} (AB)/(MN)=(BC)/(NO)=(CA)/(OM) \\ (12)/(3.6)=(10)/(3)=(15.62)/(OM) \\ \text{ simplify the last two and solve for OM :} \\ (10)/(3)=(15.62)/(OM) \\ OM=(15.62*3)/(10) \\ OM=4.686\text{ cm} \end{gathered}`

OM = 4.69 cm

In triangle MNO

MN = 3.6 cm, NO = 3 cm, OM = 4.69 cm

Answer :

MN = 3.6 cm,

NO = 3 cm,

OM = 4.69 cm