The area of a right triangle is sixty square centimetres. its base is one centimetre less than twice its height. if the base and height of the right triangle are both decreased by 2 centimetres, how much will the hypotenuse of the right triangle decrease?
1. 2 centimetres
2. 17 centimetres
3. sqrt(205) centimetres
4. 4 centimetres
5. none of the above

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

Let's find h with the quadratic formula:

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  

 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).

The base and the height are our legs. We will use "H" for the hypotenuse

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:

So, the hypotenuse decreases

c) yes, because of asa or aas