Answer:
Correct answer: hypotenuse c = 10 units
Explanation:
We will first define the variables:
The definition of an even number is 2·n where n= 1,2,3,4,........
Let the shorter leg be b = 2·n , the longer leg a = 2· n + 2 and the hypotenuse c = 2· n + 4
Write the Pythagorean Theorem:
c² = a² + b²
when we make the replacement we get
(2· n + 4)² = (2· n + 2)² + (2· n)² => 4n² + 16n + 16 = 4n² +8n + 4 + 4n² =>
4n² -8n -12 = 0 when we divide equation by 4 we get
n² - 2n - 3 = 0 => n - 3n + n - 3 => n (n - 3) + (n - 3) = (n - 3) · (n + 1) = 0 =>
n = 3 or n = - 1
We accept n = 3 and reject n = - 1 because n can only be a positive number
when we return the replacement we get three sides of ΔABC
c = 2· n + 4 = 2 · 3 + 4 = 10
a = 2· n + 2 = 2 · 3 + 2 = 8
b = 2·n = 2 · 3 = 6
Check : c - b = 10 - 6 = 4 units
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