If the question is: what is h in terms of x,
then there is no need to calculate hypotenuses; use similar triangles:
10 / 2.5 = h / [(5 - x) / 2]
4 = 2h / (5 - x)
Wrap it up...
There is a rectangle inside an isosceles triangle. One side of the rectangle is on the base of the isosceles triangle. The 2 corners on the other side of the rectangle are touching the equal lengths of the 2 isosceles triangle.
"Write down, in terms of x the height, h, of the rectangle."
Here's what I came up with:
One of the longer lengths of the triangle is which equals
Length a + length b = sqrt(106.25)
The equation becomes:
That doesn't seem correct and seems way too complex. I cannot simplify it down to just h=...
Can anyone help me?
Oh, that makes things so much simpler! Can you believe this was the hardest question for a test paper for Year 12 (about 11th the Grade) two years ago for algebra?
h = 10 - 2x
I can't believe I was overthinking it way too much, using pythagorus theorum twice... etc.