Question

what is the length of the missing side

Answer 1

Answer:

The answers are:

m = 9   and     n = 15

Step-by-step explanation:

m/15 = n/25 = 12/20

  m/15 = 12/20

  m/15 = 3/5

  5m = 45

  m = 9

  n/25 = 12/20

  n/25 = 3/5

  5n = 75

  n = 15

Answer 2

m = 9 and n = 15

Find the length( l ) of the leg in the large right triangle using Pythagoras' identity

l = √(25² - 20²) = √225 = 15

the outer and inner right triangles are similar hence the ratios of corresponding sides are equal

$\frac{25}{n}$ = $\frac{15}{m}$ = $\frac{20}{12}$

using $\frac{25}{n}$ = $\frac{20}{12}$ (cross-multiply )

20n = 300 ( divide both sides by 20 )

n = 15

using $\frac{15}{m}$ = $\frac{20}{12}$ ( cross-multiply )

20m = 180 ( divide both sides by 20 )

m = 9