The sides of a right angled triangle are of lengths x, (x + 7) and, (x + 8) cm, where x is a positive integer.
Show that x2 - 2x - 15 = 0
hence find the lengths of the sides of the triangle
x2 - 2x - 15 = 0
(x - 5)(x + 3) = 0
x = 5 or x = -3
Since x is a positive integer, x = 5
Therefore, the sides of the triangle are 5 cm, 12 cm and 13 cm.
Come on Mr. bot, you were supposed to show that x^2 - 2x - 15 = 0
not start with that equation
The sides of the right-angled triangle are given as
x, (x + 7) and, (x + 8), so clearly x+8 must be the hypotenuse
x^2 + (x+7)^2 = (x+8)^2
x^2 + x^2 + 14x + 49 = x^2 + 16x + 64
leaves us with
x^2- 2x - 15 = 0
which factors to
(x - 5)(x + 3) = 0
x = 5 or x = -3 , but since one side is x, the negative must be rejected.
if x = 5, the sides are 5, 12, and 13