Question

Find MO and PR .......................

Answer 1

MO = 12 and PR = 3

Solution:

Given $\triangle M N O \sim \Delta P Q R$.

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.

$\Rightarrow \frac{\text { Perimeter of } \triangle M N O}{\text { Perimeter of } \triangle P Q R}=\frac{M O}{P R}$

$\Rightarrow \frac{48}{12}=\frac{12 x}{x+2}$

Do cross multiplication.

$\Rightarrow 48(x+2)=12(12 x)$

$\Rightarrow 48 x+96=144 x$

Subtract 48x from both sides.

$\Rightarrow 48 x+96-48 x=144 x-48 x$

$\Rightarrow 96=96 x$

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.