The perimeter of a right-angled triangle is k times the shortest side. If the ratio of the other side to hypotenuse is 4 : 6, then what is the value of k?
A) 2 B) 3 C) 4 D) 5
Answers
Answer:
The perimeter of a right angle triangle is K times the shortest side. If the ratio of the other side to the hypotenuse is 4 : 5, then what is the value of K?
The value of k is 4
Solution:
Let "a" , "b", "c" be the length of sides of triangle
Let "b" be the shortest side
Let "c" be the hypotenuse
Perimeter of triangle = sum of length of all three sides
Perimeter of triangle = a + b + c
The perimeter of a right angle triangle is K times the shortest side
Therefore,
a + b + c = kb ------ eqn 1
The ratio of the other side to the hypotenuse is 4 : 5
a : c = 4 : 5
a = 4
c = 5
Use pythagoras theorem,
From eqn 1,
a + b + c = kb
4 + 3 + 5 = k(3)
12 = 3k
k = 4
Thus the value of k is 4
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