Answer:
5. None of the above
Step-by-step explanation:
We have this information:
A = 60 cm2
b = 2*h - 1
Let's find out b and h:
The equation of the are of a triangle is A = (b*h)/2, if we replace it with our information, we have
![60 = ((2*h - 1) * h)/2\\ 120 = 2*h^2 - h\\ 0 = 2*h^2 - h - 120](https://tex.z-dn.net/?f=60%20%3D%20%28%282%2Ah%20-%201%29%20%2A%20h%29%2F2%5C%5C%20120%20%3D%202%2Ah%5E2%20-%20h%5C%5C%200%20%3D%202%2Ah%5E2%20-%20h%20-%20120)
Let's find h with the quadratic formula:
![h = \frac{-(-1)\pm\sqrt{(-1)^2-4*2*(-120)}}{2*2} = \frac{1\pm\sqrt{961}}{4} = \frac{1\pm\ 31}{4}](https://tex.z-dn.net/?f=h%20%3D%20%5Cfrac%7B-%28-1%29%5Cpm%5Csqrt%7B%28-1%29%5E2-4%2A2%2A%28-120%29%7D%7D%7B2%2A2%7D%20%3D%20%5Cfrac%7B1%5Cpm%5Csqrt%7B961%7D%7D%7B4%7D%20%3D%20%5Cfrac%7B1%5Cpm%5C%2031%7D%7B4%7D)
h = 8 or h = -7.5
But h represents the height of the triangle, so it has to be a positive number, that's h = 8.
If we replace this in the equation we had for b, we have that b = 2*8 - 1 = 15.
Now we can calculate the hypotenuse with the Pythagorean equation
<em>The square of the length of the hypotenuse (the side opposite the right angle) of a right triangle is equal to the sum of the squares of the two legs (the two sides that meet at a right angle).
</em>
The base and the height are our legs. We will use "H" for the hypotenuse
![H^2 = b^2 + h^2 = 15^2 + 8^2 = 289\\ H = \sqrt {289} = 17](https://tex.z-dn.net/?f=H%5E2%20%3D%20b%5E2%20%2B%20h%5E2%20%3D%2015%5E2%20%2B%208%5E2%20%3D%20289%5C%5C%20H%20%3D%20%5Csqrt%20%7B289%7D%20%3D%2017)
H = 17
If we decrease the base and the height by 2 centimeters, we have
b' = 15 - 2 = 13 and h' = 8 - 2 = 6
With this, let's calculate the new hypotenuse:
![H'^2 = b'^2 + h'^2 = 13^2 + 6^2 = 205\\ H' = \sqrt {205} \approx 14.3](https://tex.z-dn.net/?f=H%27%5E2%20%3D%20b%27%5E2%20%2B%20h%27%5E2%20%3D%2013%5E2%20%2B%206%5E2%20%3D%20205%5C%5C%20H%27%20%3D%20%5Csqrt%20%7B205%7D%20%5Capprox%2014.3)
![H' \approx 14.3](https://tex.z-dn.net/?f=H%27%20%5Capprox%2014.3)
So, the hypotenuse decreases ![H - H' \approx 17 - 14.3 = 2.7](https://tex.z-dn.net/?f=H%20-%20H%27%20%5Capprox%2017%20-%2014.3%20%3D%202.7)