Question
The hypotenuse of an isosceles right triangle is 11 centimeters longer than either of its legs. find the exact length of each side.
Answer:
Step-by-step explanation:
Let the hypotenuse be y and the other legs be x.
So:
Required
Determine the exact dimension of the triangle
Using Pythagoras theorem;
This gives:
Open bracket
Collect like terms
Using quadratic formula:
Split
x can not be negative.
So:
Recall that:
Hence, the dimensions are:
1 rational solution
4x² + 12x + 9 = 0
(2x+3)²=0
2x + 3 =0
2x +3 -3 = 0-3
2x = -3
2x/x = -3/2
x = -3/2
Let the medium angle be B degrees
the small angle be A degrees
the large angle be C degrees
Then
C = 2 B + 20 ..................X
5 B = A + C ..................Y
Sum of all angles
A + B + C = 180 .............Z
Applying Y in Z
5 B + B = 180
6 B = 180
B = 30
From X C = 2 x 30 + 20 = 60 + 20 = 80
From Y 5 x 30 = A + 80
150 = A + 80
150 - 80 = A = 70
Hence medium angle B = 30 degrees
the small angle A = 70 degrees
the large angle C = 80 degrees
