Question

Find the value of x. Write an equation and
solve, showing ALL work.

Answer 1

Therefore,

∴ x = 32 units

Explanation:

Given:

Consider a Δ ABC with P and Q are the Mid points of AB and AC

AP = BP

AQ = CQ

PQ = 48

BC = 3x

To Find:

x = ?

Solution:

Mid Point Theorem :

The Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.

i.e Here by Mid Point Theorem we will have

`PQ=(1)/(2)BC\\`

Substituting the values we get

`\therefore 48 =(1)/(2)* 3x\\ \\\therefore 48* 2 =3x\\\\\therefore x =(96)/(3)\\\\\therefore x =32\ units`

∴ x = 32 units