Question

Can you help me please ​

Answer 1

x = 7

Explanation:

The parameters of the triangle having bisected angle are;

The length of the opposite and adjacent side of one of the halves of the bisected angle = 6 and 14 respectively

The length of the opposite and adjacent side of the other half of the bisected angle = (3·x - 12) and 21 respectively

By the angle bisector theorem, we have;

`(14)/(6) = (21)/(3\cdot x - 12)`

Simplifying, we get;

`(14)/(6) = (2 * 7)/(2 * 3) = (7)/(3)`

`(21)/(3\cdot x - 12) = (3 * 7)/(3 * (x - 4)) = (7)/(x - 4)`

`(7)/(3) = (7)/( x - 4)`

7 × (x - 4) = 3 × 7

∴ x - 4 = 3

x = 3 + 4 = 7

x = 7.