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.

$\Rightarrow \frac{\text{Perimeter of }\triangle MNO}{\text{Perimeter of }\triangle PQR} =\frac{MO}{PR}$

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

Do cross multiplication.

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

$\Rightarrow 48x+96= 144x$

Subtract 48x from both sides.

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

$\Rightarrow 96= 96x$

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.