pls answer! math sucks

Question

A ladder is leaning against a building. The distance from the bottom of the ladder to the building is 8 ft less than the length of the ladder. How high up the side of the building is the top of the ladder if that distance is 1 ft less than the length of the​ ladder?

Answer 1

Hi Wade B.

Draw your figure, you should get a Right Triangle. The description above forms a Right Triangle, use the Pythagorean theorem to solve for the value, keep in mind that the length that you need cannot be negative

a² + b² = c²

Let c = the longest side where the ladder is slanted against the building

Let a = height, how high up the side of the building the top of the ladder is; c - 1

Let b = base, the distance from the bottom of the ladder to the building; c - 8

(c - 1)² + (c - 8)² = c²

Work through each set of parenthesis

Combine like terms

Factor where required

Solve for c

Keep in mind c should be positive when you plug it back into (c -1) and (c - 8)

Answer 2

Come on, math is cool! You have to learn the rules of the game.

Draw a diagram of the situation. Label the length of the ladder as L.

Label the distance of the bottom of the ladder to the building as L-8.

Label the height of the ladder up the wall as L - 1.

Note that the ladder, ground, and wall make a right triangle with the ladder as the hypotenuse.

Set up the Pythagorean theorem, L² = (L-8)² + (L-1)².

Square the parentheses. L² = L² -16L +64 + L² -2L +1

Combine like terms and set results equal to zero. L² -18L +65 = 0.

This is a quadratic equation that can be solved for L either by factoring or the quadratic formula. Let's try factoring. The equation above can be factored into (L - 13) (L - 5) =0. Each parenthesis can be set equal to zero for the whole equation to equal zero. This gives L = 13 or L = 5. So, which one is correct?

If we use L = 5, this makes the distance of the foot of the ladder to the wall = -8! So, the real answer is L = 13 ft.