SOLUTION: I just don't get word problems! the two sides of a right triangle differ by one. If the hypotenuse is 29cm, then determine the lengths of the two sides. How do I solve using the qu

Question 324504: I just don't get word problems! the two sides of a right triangle differ by one. If the hypotenuse is 29cm, then determine the lengths of the two sides. How do I solve using the quadratric formula.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
"the two sides of a right triangle differ by one" means that the two legs of the triangle are 'x' and 'x+1'

Since "the hypotenuse is 29cm", we know that by the pythagorean theorem, we get the equation

Start with the given equation.

Square 29 to get 841

FOIL

FOIL

Subtract 841 from both sides.

Combine like terms.

Notice that the quadratic is in the form of where , , and

Let's use the quadratic formula to solve for "x":

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the possible solutions are or

Since a negative length doesn't make sense, this means that we're going to ignore

So this means that one leg is cm long. So the next leg is cm long.

So the lengths of the two legs are 20 cm and 21 cm.
RELATED QUESTIONS
The two sides of a right triangle differ by one. If the hypotenuse is 29cm, then... (answered by MRperkins,palanisamy)

hey, could you please solve the following two problem for me, and thanks, 1. What... (answered by checkley77)

I have a hard time with word problems. A right triangle is a triangle with one angle... (answered by stanbon)

The legs of a right triangle differ by 2 cm. and the hypotenuse is 4 cm. more than the... (answered by MRperkins)

The legs of a right triangle differ by 2 centimeters and the hypotenuse is 4 centimeters... (answered by jojo14344)

if one side of a triangle is double the other and the angles opposite these sides differ... (answered by drk)

The legs of a right triangle differ by 2 cm. and the hypotenuse is 4 cm. more than the... (answered by MRperkins)

Suppose the measures of the two legs of a right triangle differ by 2 inches and that the... (answered by Fombitz)

i hate word problems. A restaurant purchased eight tablecloths and five napkins for... (answered by Mathtut,HyperBrain)