Please help me solve this question.

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'.
-- 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.

Height =2x so we must find x then multiply by 2

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

so x=13.0008
2x=height=26.0016