Answer:
26cm, 24cm, 10cm
Explanation:
We can use pythagorean theorem to find the equation for the missing side:
a² + b² = c²
n² + missingside² = (2n + 6)²
missingside² = (2n + 6)² - n²
missingside = √[(2n + 6)² - n²]
Now, we know that adding all the sides together should give us 60 (because the perimeter is 60). So, let's write that as an equation:
n + 2n + 6 + √[(2n + 6)² - n²] = 60
now, solve for n:
√[(2n + 6)² - n²] = 60 - n - 2n - 6
√[(2n + 6)² - n²] = 54 - 3n
(2n + 6)² - n² = (54 - 3n)²
4n² + 24n + 36 - n²= 54² - 324n + 9n²
9n² - 3n² - 324n -24n + 54² - 36 = 0
6n² - 348n + 2880 = 0
n² - 58n + 480 = 0
n = 10, n = 48
So have 2 values for n, so we need to see which one works. If we plug both 10 and 48 into our original equation (n + 2n + 6 + √[(2n + 6)² - n²] = 60), we see that only 10 works, not 48. So, n=10.
Now, let's plug n=10 into the equation for each side:
Hypotenuse:
2n + 6 = 2(10) + 6 = 26
Other side:
n = 10
Last side:
√[(2n + 6)² - n²] = √[(2(10) + 6)² - (10)²] = 24
And 26 + 24 + 10 = 60, so we have found the lengths of each side! Let me know if you have other questions about the steps.