Expert: Richard J. Raridon - 1/30/2008

Question
hello, can you please explain to me how to solve word problems using both the quadric formula and the Pothagorean theorem? and the area of a rectangle with the quadric formula?

for example:  the hypothenuse of a right triangle is 26 feet long, one leg is 14 ft longer than the other. find the lengths of the legs of the triangle.

and: the width of a rectangle is 3 in. less than its length, and the area is 340 square. inches. what are the length and width?

please help me.
thank you, Kayley age-15

Answer
The Pythagorean theorem states that for a right triangle,
x^2 +y^2 = h^2 where x and y are the two sides and h is the hypotenuse.  So for this problem, y = x+14 and you have
x^2 +(x+14)^2 = 26^2
x^2 +14x -240 = 0 = (x+24)(x-10) so x=10 and y=24

L = W+3 and LW = 340
(W+3)W = 340
W^2 +3W -340 = 0 = (W+20)(W-17) so W = 17, L = 20