A right triangle has an area of 380 square centimeters.Its perimeter is 100 centimeters. Find the vertex angle formed of the hypotenuse and the base of the triangle. Also find the length of the hypotenuse.
1/2bh=380=>bh=760
b+h+c=100=>c=100-(b+h)
And c²=b²+h²
Factors of 760 are possible of b and h
76*10,then c=100-86=14 (error)
38*20,then c=100-58=42 (38,20,42 are not triple of pythagoras)
19*40,then c=41 (19,40,41 are triple of pythagoras)
Hence the length of the hypotenuse is 41cm
760
76 10
2 38 10
2 2 19 2 5
40
19
41
20
38
1/2bh=380=>bh=760
b+h+c=100=>c=100-(b+h)
And c²=b²+h²
Factors of 760 are possible of b and h
76*10,then c=100-86=14 (error)
38*20,then c=100-58=42 (38,20,42 are not triple of pythagoras)
19*40,then c=41 (19,40,41 are triple of pythagoras)
Hence the length of the hypotenuse is 41cm