Mike McClenathan

In an isosceles triangle with a height 10 and a base 10, a square is inscribed with side x along the base of the triangle as shown above. What is the area of the square?

Posted:

I’ll draw this as best I can:   Look OK? Now let me draw a few more segments in blue… See what’s going on there? All of the small triangles in the figure are the same! (You can prove this with triangle similarity/congruence rules easily enough—I won’t spend the time doing so here, though.) We (more…)

satfanatic

Regarding triangles question number 8 in your book…

Posted:

I don’t know how to navigate your site yet, so please forgive me if you have already answered this question. Regarding question number 8 in your book, will you further explain why y=180-x is the same angle degree as the unmarked angle? I know y=2x because of geometry, but I do not understand how y can also equal x?

Lena

Triangles ABC and ABD share side AB…

Posted:

Triangles ABC and ABD share side AB.
Triangle ABC has area Q and triangle ABD has area R. If AD is longer than AC and BD is longer than BC, which of the following could be true?
I-R> Q
II R=Q
III R < Q
I chose "I" only but the answer was E (all of them could be.) How can the second and third condition be true?
Thanks in advance!

esedlin

Hi Mike,question on Math Quiz 4 #9: I get the answer and the proposed solution (area of large triangle minus area of small triangle)…

Posted:

Hi Mike,
question on Math Quiz 4 #9: I get the answer and the proposed solution (area of large triangle minus area of small triangle). But my daughter worked the problem differently and I think what she did was correct, but she got a slightly different answer and I can’t figure out exactly why.
Her solution: she used Pythag Theorem to get the hypot of small triangle: so 4^2 + 1^2 = c^2…. so c=Sqrt(17). This is base of large triangle. So A= 1/2 bXh, or 1/2 (sqrt 17)(8), she got 16.492.