Question

3. Consider the following diagram.

Answer 1

Answer:

m = 3, n = 6

Step-by-step explanation:

The hypotenuse leg (HL) theorem states that two triangles are said to be similar if one leg and the hypotenuse of the triangles are congruent.

From the diagram, comparing the hypotenuse of the triangles;

4m + 1 = 13

4m = 13 - 1

     = 12

m = $\frac{12}{4}$

   = 3

m = 3

Also, comparing the sides;

2m + n = 8m - 2n

substitute the value of m to have,

6 + n = 24 - 2n

collect like terms,

n + 2n = 24 - 6

3n = 18

n = $\frac{18}{3}$

    = 6

n = 6

m = 3, n = 6