Question

find the value of $x$.
7.
8.
9.
triangle angle-bisector theorem if a ray bisects an angle of a triangle, then it divides the opposite side into segments proportional to the other two sides.

example 3
find the value of $x$.
solution
$\frac{x}{40 - x} = \frac{27}{45}$
$\frac{x}{40 - x} = \frac{3}{5}$
$5x = 120 - 3x$
$8x = 120$
$x = 15$

find the value of $x$.
10.
11.
12.

Explanation:

Problem 7

Step1: Set up proportional equation

$\frac{x}{12.5} = \frac{12}{15}$

Step2: Simplify and solve for x

$x = 12.5 \times \frac{12}{15} = 12.5 \times 0.8$
$x = 10$

Problem 8

Step1: Set up proportional equation

$\frac{x-5}{8} = \frac{5}{4}$

Step2: Solve for x

$x-5 = 8 \times \frac{5}{4}$
$x-5 = 10$
$x = 15$

Problem 9

Step1: Set up proportional equation

$\frac{x+10}{x} = \frac{27}{18}$

Step2: Simplify and solve for x

$\frac{x+10}{x} = \frac{3}{2}$
$2(x+10) = 3x$
$2x + 20 = 3x$
$x = 20$

Problem 10

Step1: Set up proportional equation

$\frac{x}{24-x} = \frac{12}{18}$

Step2: Simplify and solve for x

$\frac{x}{24-x} = \frac{2}{3}$
$3x = 2(24-x)$
$3x = 48 - 2x$
$5x = 48$
$x = 9.6$

Problem 11

Step1: Set up proportional equation

$\frac{x}{12.5} = \frac{8}{10}$

Step2: Solve for x

$x = 12.5 \times \frac{8}{10}$
$x = 10$

Problem 12

Step1: Set up proportional equation

$\frac{x}{15-x} = \frac{10}{20}$

Step2: Simplify and solve for x

$\frac{x}{15-x} = \frac{1}{2}$
$2x = 15 - x$
$3x = 15$
$x = 5$

Answer:

Problem 7: $x=10$
Problem 8: $x=15$
Problem 9: $x=20$
Problem 10: $x=9.6$
Problem 11: $x=10$
Problem 12: $x=5$