Question

How do you find area of a triangle when there's variables?!?!?

Please give answer and explanation on how you got there so i learn

Answer 1

Explanation:

Good day,

First, I would like to commend you for wanting to learn instead of just asking for the answer. That is a good attitude to have. Moving on, I feel like there are plenty of ways to solve this, but this is how I solved for it. I will try to explain it as best as I can

First concept that we need to understand is the Pythagorean theorem, in case you have forgotten it is
`a^(2)+b^(2) =c^(2)`. wherein "c" is the hypotenuse, which in your question is 3x-11. While "a" and "b" are 13 and 2x+20. SO let us input it into the Pythagorean theorem.

This gives us

`13^(2) +(2x+20)^(2) =(3x-11)^(2)`

Now we have to isolate x

First subtract (2x+20) on both sides

`13^(2)+(2x+20)^(2)-(2x+20)^(2)=(3x-11)^(2)-(2x+20)^(2)`

This gives us

`13^(2) =(3x-11)^(2) -(2x+20)^(2)`

Now we answer the squared values

`13^(2) =169`

`(3x-11)^(2) =(3x-11)(3x-11)=9x^(2) -33x-33x+121`

`(2x+20)^(2) =(2x+20)(2x+20)=4x^(2) +40x+40x+400`

Now Let's look at it at the equation again

`169=9x^(2) (-33x-33x+121)-(4x^(2) +40x+40x+400)`

Distribute the negative sign in
`-(4x^(2) +40x+40x+400)` which gives us

`169=9x^(2) -33x-33x+121-4x^(2) -40x-40x-400`

Now let us combine the like terms

`169=5x^(2) -146x-279`

Subtract 169 on both sides

`0=5x^(2) -146x-448`

To get the x value I used the quadratic formula. Just look it up in the internet to find the formula.

in the quadratic formula you need to input values into 3 variables. a, b, and c. From what we calculated earlier in
`0=5x^(2) -146x-448`, a=5, b=-146, and c=-448

when you input that into the quadratic formula, you will get the answer of x=32, and x=
`-(14)/(5)`. We will get 32 as our value, because when we input
`-(14)/(5)` into let's say 3x-11 we get a negative value, and we can't have a negative distance.

So, input 32 into the values of x and you'll get the measurements of the sides. Then, I imagine you already know how to get the area of a triangle. I am not sure if I have over complicated the process of getting the answer, but here you go. Good luck and study well.