Answer:
The answers are;
m = 9, e = 9
Step-by-step explanation:
The question relates to right triangles with special properties;
The given parameters of the given right triangles are;
The measure of an interior angle of the triangle = 45°
The length of the given leg length of the triangle = (9·√2)/2
The length of the other leg length of the triangle = n
The length of the hypotenuse side = m
A right triangle with one of the measures of the interior angles equal to 45° is a special triangle that has both leg lengths of the triangle equal
Therefore;
The length of the other leg of the right triangle = n = The length of the given leg of the triangle = (9·√2)/2
∴ n = (9·√2)/2
n = (e·√f)/g
Therefore, by comparison, we have;
e = 9, f = 2, and g = 2
By Pythagoras's theorem, we have;
m = √(n² + ((9×√2)/2)² = √((9×√2)/2)² + ((9×√2)/2)²) = √(81/2 + 81/2) = √81 = 9
m = 9.