Question

One side of a triangle is 4cm longer than another side. The ray bisecting the angle between these sides divides the opposite side into 5cm and 3cm segments. The 5cm segment is adjacent to the longer of the two sides. Find the perimeter of the triangle.

Answer 1

24 cm

Explanation:

A figure has been drawn and attached below to represent the information given in the question.

Let the shorter side represent x.

The other longer side = x + 4

Thus, the following equation below would enable us solve for x.

`(x)/(x + 4) = (3)/(5)` (Angle Bisector Theorem)

Cross multiply

`5(x) = 3(x + 4)`

`5x = 3x + 12`

Subtract 3x from both sides

`5x - 3x = 12`

`2x = 12`

Divide both sides by 2

`x = 6`

Perimeter = (x + 4) + x + 5 + 3

Plug in the value of x

Perimeter = 6 + 4 + 6 + 5 + 3

Perimeter = 24 cm