Question

Proportions in Triangles

Answer 1

You could use the Pythagorean theorem to solve this since we know that for both triangles, we have one side that is equal

Answer 2

It says solve for x in the picture

Answer 3

How would I apply the Py Theorm?

Answer 4

It looks like if we apply what I said then we can see that the B's in the triangles using the pythagorean theorem match and because they are equal...we can solve for B and put the two equations equal to each other

Answer 5

.... its a different language to me DX

Answer 6

Lol sorry if I couldnt explain it well and I apologize but I need to leave since I am at school and it is late lol...it looks like genius12 can help though since it seems like he is typing a lot

Answer 7

Thanks anyways :)

Answer 8

All right so to solve for x, we can use the Pythagorean Theorem. This is because when straight vertical line is drawn through the triangle, it creates 2 right angles on either sides.
We now have 2 smaller triangles, both with 1 right angle so we can use the pythagorean theorem with either of them.

Since the theorem states: a^2 + b^2 = c^2, where c is the hypotenuse and a, b are the other two sides in the triangle. We choose to solve for x using the smaller right triangle on the right. We know it's hypotenuse (the longest side of a right triangle) is 7x, so c = 7x. We also know that one of it's other sides is 5x + 3. So we can call either a or b 5x+3, but I'll in this case call a = 5x + 3. Since we know what a and c are, we can solve for the third side b and as a result, solve for x.

a^2 + b^2 = c^2
(5x+3)^2 + b^2 = (7x)^2
(25x^2 + 30x + 9) + b^2 = 49x^2
b^2 = 49x^2 - (25x^2 + 30x + 9)
= 24x^2 - 30x - 9

So we know what b^2, or the length of the missing side squared for smaller right triangle on the right. We also notice that both triangles on the right and left share the same missing side, therefore, the b^2 value for both triangles should be the same. So now we get the value of b^2 using the hypotenuse and the other given side of the right triangle on the left with a = 8x and c = 10x - 2

a^2 + b^2 = c^2
(8x)^2 + b^2 = (10x-2)^2
(64x^2) + b^2 = 100x^2 - 40x + 4
b^2 = 100x^2 - 40x + 4 - (64x^2)
= 36x^2 - 40x + 4

Since both triangles share the exact same missing side, then the value of b^2 in both triangles is the same. Since we know that b^2 = 24x^2 - 30x - 9 from the right triangle on the right, and we know that b^2 = 36^2 - 40x + 4, then we know that both equations are the same and equal since they represent the same value of the same side. Thus, we can equate the two equations and solve for x.

24x^2 - 30x - 9 = 36x^2 - 40x + 4

Bring everything one side to get a single quadratic.

12x^2 - 10x + 13 = 0 ---> Now just factor the quadratic to get possible values of x.

We are looking for two numbers that multiply to (12 x 13) which 156 and to -10. We notice that we can't factor this quadratic normally, and so we use the quadratic formula to get the values of x. Can you carry it on from here?

Answer 9

@meadowlark If you need ever more help and can't figure what to do at this point, just ask.

Answer 10

Thank you so much