Question

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?

Answer 1

Answer:

Step-by-step explanation:

Answer 2

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,

$hypotenuse^2 = opposite^2 + adjacent^2$

$(5)^2 = (4)^2 + b^2\\\\25 = 16 + b^2\\\\b^2 = 25 - 16\\\\b^2 = 9\\\\b = 3$

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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