if we cut the triangle in half from with the line from left to right, we have a trianlgle that is x high and 2x+7 wide and the hyposonuse that is 35.47 so a^2+b^2=c^2 x^2+(2x+7)^2=35.47^2 x^2+4x^2+28x+49=1258.12 group like terms 5x^2+28x+49=1258.12 subtract 1258.12 from both sides 5x^2+28x-1209.12=0 factor 5(x-13.0008)(x+18.6008)=0 therefore (x-13.0008) or/and (x+18.6008)=0 x-13.0008=0 add 13.0008 to both sides x=13.0008
x+18.6008=0 subtract 18.6008 from both sides x=-18.6008 since heights cannot be negative, this solution can be discarded
Cut the sign in half across its middle. Then you have two right triangles. They're congruent, so pick one to work with, and discard the other one temporarily.
In the right triangle:
-- The length of one leg is 'x'.<em /> -- The length of the other leg is (2x + 7). -- The length of the hypotenuse is 35.47 inches.
You know that in any right triangle:
(The square of the hypotenuse) = (the square of one leg) + (the square of the other one.)
so you can use that to find the value of 'x'.
One you know the value of 'x', go back to the whole sign before you cut it in half, and notice that the height of the sign is '2x' ... which is the answer.
