What is the hypotenuse if one leg is 8 ft and the other leg is 2 ft less than the hypotenuse?

Answer 1

This problem can be solved with some simple Algebra and the Pythagorean Theorem: a^2+b^2=c^2 (a and b are the two legs, and c is the hypotenuse).

Let's start by just putting what we have into the equation

8^2+b^2=c^2.

Now we are going to see if we can eliminate our problem to only one variable. We are told that fhe leg (b) is 2 ft less than the hypotenuse (c). So we'll convert this into an equation:

c-2=b.

Now we will substitute b for c-2.

8^2+(c-2)^2=c^2

Simplify:

64+c^2-4c+4=c^2

Combine Like Terms:

64+4+c^2-4c=c^2

68+c^2-4c=c^2

Get our variable (c) on one side of the equals sign:

68+c^2-4c = c^2

-c^2+4c =-c^2+4c

Simplify:

68=4c

Divide both sides by 4.

17=c

Now we say our hypotenuse is 17, but we can check our answer. We know b is 2 less than 17, so b is 15.

a^2+b^2=c^2

8^2+15^2=17^2

64+225=289

This is correct, therefore 17 is our hypotenuse.

Answer 2

You need to write an equation to express the given facts, and then solve it. You can use the Pythagorean theorem:(leg 1) squared + (leg 2) squared = hypothenuse squared

Filling in the facts you know, and calling the hypothenuse "h":

8 squared + (h-2) squared = h squared

or:

64 + (h-2) squared = h squared

Solve this equation, and you get the hypothenuse.