solve the problem please.....
Picture this as a right triangle. The "distance from the wall" (i.e. the ground) is the bottom of the triangle, and the ladder is the hypotenuse. You are given the height as 6 ft, so this is the third side of the triangle.
Let x equal the ground / base of the triangle.
Because this is a right triangle, we can use the Pythagorean theorem (a2 + b2 = c2), where a and b are the two sides making the right angle, and c is the hypotenuse.
We are given in the problem that x is two feet more than the ladder / hypotenuse. So c = x+2. One side of triangle can be a, and the other b. Let's say that a is the height, which is given as 6, and b is the ground, which we are calling x:
a=6 b=x c=x+2
Plug this into the Pythagorean theorem: 62 + x2 = (x+2)2
First, simplify the right side by expanding it:
(x+2)2 = (x+2)(x+2) = x2 + 4x + 4
62 + x2 = 36 + x2 = x2 + 4x + 4
Subtract 4 from both sides: 32 + x2 = x2 + 4x
Subtract x2 from both sides: 32 = 4x
Divide both sides by 4: 8 = x
Remember that x was equal to the distance from the wall, and the length of the ladder is two feet more than x.
Therefore, the length of the ladder = x+2 = 8+2 = 10 feet.