Question

What is the length of the missing side

Answer 1

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

`(25)/(n)` =
`(15)/(m)` =
`(20)/(12)`

using
`(25)/(n)` =
`(20)/(12)` (cross-multiply )

20n = 300 ( divide both sides by 20 )

n = 15

using
`(15)/(m)` =
`(20)/(12)` ( cross-multiply )

20m = 180 ( divide both sides by 20 )

m = 9

Answer 2

The answers are:

m = 9 and n = 15

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