The architect's side view drawing of a saltbox-style house shows a post that supports the roof ridge. The support post is 15 ft tall. The distance from the front of the house to the support post is less than the distance from the post to the back of the house. How far from the front of the house is the support post positioned?

21 ft

Step-by-step explanation:

We are given that the support post is 10 ft tall.

Let x represents the distance between the support post and the front of the house, that means that 25-x will be the distance from back.

By Geometric Mean Theorem, the length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse.

So, by the previous Theorem, we get:

We got that the distance between the support post and the front of the house is 4 ft, while the distance between the support post and the back of the house is ft.    

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb

there should be an link icon on the bottom of the text box you get. it looks like a paperclip!