Question

the area of a kite is (2x²+9x+4)cm² if the lenght of one of its diagonals is (x+4)cm find the measure of the other base.

Answer 1

The area of a kite is A = (1/2)(d1)(d2) where d1 and d2 are the lengths of the diagonals.
You have A = 2x^2 + 9x + 4 and d2 = x + 4, and you need d1, so
(1/2)(d1)(d2) = A
(1/2)(d1)(x + 4) = 2x^2 + 9x + 4
Multiply both sides by 2
(d1)(x + 4) = 2(2x^2 + 9x + 4)
Now divide both sides by x + 4
d1 = ( 2(2x^2 + 9x + 4) )/(x + 4)
Factor 2x^2 + 9x + 4
d1 = (2(2x + 1)(x + 4))/(x + 4)
d1 = 2(2x + 1)
d1 = 4x + 2

Answer 2

thanks :)