Question

What is the value of x?

Answer 1

Answer: x = 15

Step-by-step explanation: The first thing to note is that what we have here are two similar triangles. First we have triangle ABC and secondly we have triangle EDC. Line BD is a transversal that cuts line AE at point C. Hence we can deduce that angle ACB is equal in measurement to angle ECD (opposite angles). Next we also observe that the other two angles are right angles, that is, 90° in size. Therefore we can conclude that the other two angles (angle ABC and angle EDC) are also of the same measurement.

We can now establish the ratio of the similar sides.

Line AB = Line ED

Line AC = Line EC

AB/ED = AC/EC

24/40 = 2x/3x + 5

3/5 = 2x/3x + 5 {the left hand side has been reduced to it's simplest form}

Next we cross multiply and that gives us

3(3x + 5) = 5(2x)

9x + 15 = 10x

Subtract 9x from both sides of the equation

15 = 10x - 9x

15 = x