Using the Pythagorean theorem a^2 + b^2 = C^2
a and b are the base and height and C is the hypotenuse of the triangle.
Base = a = 10 cm
Height = b = x
Hypotenuse = c = 7 + x
So we get 10^2 + x^2 = (7+x)^2
= 100 + x^2 = (7+x)^2
Subtract (7+x)^2 from each side:
100 + x^2 - (7+x)^2 = 0
Rewrite (7+x)^2 as (7+x) (7+x)
100 + x^2 + ((7+x) (7+x)) = 0
use FOIL on: ((7+x) (7+x))
((7+x) (7+x)) = (49 +14x +x^2)
Now yo have:
100 + x^2 - (49 +14x +x^2) = 0
Apply Distributive Property:
100-49 = 51
x^2 - x^2 = 0
Now you have:
51-14x =0
Rewrite the left side to get the variable first:
-14x+51 = 0
Subtract 51 from each side:
-14x = -51
Divide each side by -14:
x = 51/14
x = 3.64
Rounded to the nearest tenth X = 3.6