Question

Length of the median CP

Answer 1

Given:

ΔABC $\sim$ ΔDEF

To find:

The length of median CP

Solution:

In ΔABC,

AP = 12, BP = 12 and PC = 3x - 12

In ΔDEF,

DQ = 16, QE = 16 and FQ = 2x + 8

If two triangles are similar, then their median is proportional to the corresponding sides.

$\Rightarrow \frac{AP}{DQ} =\frac{PC}{FQ}$

$\Rightarrow \frac{12}{16} =\frac{3x-12}{2x+8}$

Do cross multiplication.

$\Rightarrow 12(2x+8)=16(3x-12)$

$\Rightarrow 24x+96=48x-192$

Add 192 on both sides.

$\Rightarrow 24x+96+192=48x-192+192$

$\Rightarrow 24x+288=48x$

Subtract 24x from both sides.

$\Rightarrow 24x+288- 24x=48x- 24x$

$\Rightarrow 288=24x$

Divide by 24 on both sides.

⇒ 12 = x

Substitute x = 12 in CP.

CP = 3(12) - 12

     = 36 - 12

     = 24

The length of median CP is 24.