Question

Given a right triangle with one leg length of a, one leg length of x-3 and the hypo is x, how does a affect x? Shown on a graph.

I solved for a, it is equal to the square root of 6x-9.... I am having a difficult time interpreting how a affects x.. I am not sure how to graph

Answer 1

Solution:

Let ABC be the given right triangle, with angle B=90 degree. It is given that,

One leg, let's say BC=a, other leg AB=(x-3) and hypotenuse AC=x

Then by Pythagoras theorem , AB^2 + BC^2 = AC^2

(a)^2 + (x-3)^2 = (x)^2

a^2 + x^2-6x+9=x^2

a^2+x^2-X^2-6x+9=0

a^2-6x+9=0

a^2+9=6x

x=a^2+9/6...........................(1)

Now we can find how does a affect x.

Let's calculate values of x at different values of a and we can just find how a affects the x.

1) Let a=1, plugging value of a=1 in equation (1) we get : x=1^2+9/6 = 1.78

2) Let a=2, plugging value of a=2 in equation (1) we get : x=2^2+9/6 = 2.17

3) Let a=3, plugging value of a=3 in equation (1) we get : x=3^2+9/6=3

4) Let a=4, plugging value of a=4 in equation (1) we get : x=4^2+9/6 = 4.17

............... and so on we can calculate the value of x for different values of a, and now we can see how it affects.

Conclusion: As value of a increases value of x also increases and will always be greater than a.

---------------------------------------------------------------------- thanks