Question

Solve for x. (Geometry)

Answer 1

Hello from MrBillDoesMath!

Answer:   9

Discussion

By the Pythagorean theorem, the length of the third side (the hypotenuse) in the triangle with sides 4 and 6 is sqrt ( 4^2 + 6^2) = sqrt (52)

Applying Pythagoras to the left most triangle (sides, x and 6) gives:

x^2 + 6^2 = m^2     (I am calling the unknown side "m)

Finally, in the big right triangle (the one containing the two right triangles)

(x + 4) ^2  =   (sqrt(52)) ^2  + m^2

OK!   Subtract the first equation from the second:

   (x+4)^2             = 52 + m^2

   x^2     + 36      =          m^2

-----------------------------------------------------

( x+4)^2 - x^2 - 36 = 52 + (m^2 - m^2)  =>

x^2 + 8x + 16  - x^2 -36 = 52  =>

x^2 - x^2 + 8x + 16 -36 = 52 =>

0 +              8x - 20       = 52 =>

8x = 72 =>

x = 9

Thank you,

MrB