summer question practice #2

[Guest]

Here is another question my son is confused on. I don't understand any written problems so I can't help him practice.

The hypotenuse of a right triangle is 2 ft less than three times the shorter leg. The longer leg is 3 ft. less than three times the shorter leg. Find the length of the shorter leg.

He understands that this goes by the Pythagorean Theorem a^2 + b^2=C^2 and c is the hypotenuse, b is the longer leg, and a is the shorter. That is all he understands. Any help would be greatly appreciated.

 

[TchrWill]

Let the three sides be a, b and c with a being the short side.

Then, b = 3a - 3 and c = 3a - 2.

From the Pythagorean Theorem, a^2 + b^2 = c^2 making a^2 + (3a - 3)^2 = (3a - 2)^2.

Expanding and simplifying, you will end up with a quadratic equation solvabe by means of the quadratic formula or factoring.

 

[Guest]

Great

My son said that did help him and I am glad because I still don't get it.

 

[Denis]

Re: Great

My son said that did help him and I am glad because I still don't get it.

What do you not get?
You said you understood that a^2 + b^2 = c^2. [1]
You seem to understand that b = 3a - 3 and c = 3a - 2;
so substituting that back in [1] gives:
a^2 + (3a - 3)^2 = (3a - 2)^2

(3a - 3)^2 = (3a - 3) times (3a - 3) = 9a^2 - 18a + 9
(3a - 2)^2 = (3a - 2) times (3a - 2) = 9a^2 - 12a + 4

a^2 + 9a^2 - 18a + 9 = 9a^2 - 12a + 4
a^2 - 6a + 5 = 0
(a - 5)(a-1) = 0
a = 5 or a = 1; 1 is impossible, so a = 5

Therefore, b = 3a - 3 = 12 and c = 3a - 2 = 13
5^2 + 12^2 = 13^2
25 + 144 = 169

Did that help?