Problema Solution
The hypotenuse of a right triangle is 4 cm longer than one leg and 8 cm longer than the other leg. Let x represent the length of the hypotenuse.
A. Write an expression for the length of each leg in terms of x?
B. Use the Pythagorean Theorem to write an equation that can be solved for x.
C. find the solutions of your equation from part b.
D. What do the solutions of your equation represent? Are both solutions reasonable? Explain.
Answer provided by our tutors
A.
The length of the first leg is: x - 4
The length of the second leg is: x - 8
B.
(x - 4)^2 + (x - 8)^2 = x^2
C.
click here to see the above equation solved for x
........
x1 = 20
x2 = 4
D.
The solution x = 20 cm is reasonable since 20 - 4 = 16 >0 and 20 - 8 = 12 > 0.
The solution x = 4 cm in note reasonable since 4 - 4 = 0 and 4 - 8 = - 4 < 0 and we know that the lengths of the legs are always positive.