MO = 12 and PR = 3
Solution:
Given [tex]\triangle M N O \sim \Delta P Q R[/tex].
Perimeter of ΔMNO = 48
Perimeter of ΔPQR = 12
MO = 12x and PR = x + 2
If two triangles are similar, then the ratio of corresponding sides is equal to the ratio of perimeter of the triangles.
[tex]$\Rightarrow \frac{\text { Perimeter of } \triangle M N O}{\text { Perimeter of } \triangle P Q R}=\frac{M O}{P R}[/tex]
[tex]$\Rightarrow \frac{48}{12}=\frac{12 x}{x+2}[/tex]
Do cross multiplication.
[tex]\Rightarrow 48(x+2)=12(12 x)[/tex]
[tex]\Rightarrow 48 x+96=144 x[/tex]
Subtract 48x from both sides.
[tex]\Rightarrow 48 x+96-48 x=144 x-48 x[/tex]
[tex]\Rightarrow 96=96 x[/tex]
Divide by 96 on both sides, we get
⇒ 1 = x
⇒ x = 1
Substitute x = 1 in MO an PR.
MO = 12(1) = 12
PR = 1 + 2 = 3
Therefore MO = 12 and PR = 3.
