One side of a triangle is 5cm more than the other and 2cm less than the hypotenuse. Find the lengths of the 3 sides?
let the shortest side be x
then the longer side is x+5 and the
hypotenuse is x+7
(x+7)^2 = x^2 + (x+5)^2
x^2 + 14x + 49 = x^2 + x^2 + 10x + 25
x^2 - 4x - 24 = 0
x^2 - 4x + .... = 24 + ... , going to complete the square
x^2 - 4x + 4 = 24+4 = 28
(x+2)^2 = 28
x-2 = ± √28
x = ±√28 + 2
can't have a negative side, so x = √28 - 2
the sides are √28 + 2 , √28 + 7, and √28+9
or appr 7.29 , 12.29, and 14.29
check:
14.29^2 = 204.20
12.29^2 + 7.29^2 = 204.19 , close enough for 2 decimal accuracy
the third last line of the solution should of course be
(x-2)^2 = 28
and the conclusion line:
can't have a negative side, so x = √28 + 2
Let's assume that the length of one side of the triangle is x cm.
According to the given information, we can deduce the following:
1. One side is 5 cm more than the other side:
So, the length of the other side is (x + 5) cm.
2. One side is 2 cm less than the hypotenuse:
So, the length of the hypotenuse is (x + 2) cm.
Now, we know that a triangle has three sides: the base, the height, and the hypotenuse. In this case, we can assign the sides as follows:
Base: x cm
Height: (x + 5) cm
Hypotenuse: (x + 2) cm
The Pythagorean theorem allows us to find the relationship between the sides of a right triangle. According to the theorem, the sum of the squares of the base and the height is equal to the square of the hypotenuse:
(x^2) + [(x + 5)^2] = (x + 2)^2
Now, we can solve the equation to find the value of x.