One end of a 13-foot-long ladder is resting on the top of a vertical wall. The distance from the foot of the ladder to the base of the wall is 7 feet less than the height of the wall. How high is the wall

Height of wall is 12 ft.

Explanation:

In the shown figure, AB denotes the height of the wall, BC denotes the distance between foot of the ladder and wall and AC denotes the length of the ladder.

Let h be the height of wall. By Pythagoras Theorem,

(AB)² + (BC)² = (AC)²

According to the problem, AC = 13 ft, AB = h ft and BC = (h - 7) ft:

h² + (h-7)² = (13)²

h² + h² + 49 - 14h = 169

2h² - 14h - 120 = 0

h² - 7h - 60 = 0

By mid-term splitting,

h² - 12h + 5h - 120 = 0

h(h - 12) + 5(h - 12) = 0

(h - 12) x (h + 5) = 0

h = 12 ft or h = -5 ft

Since, height of wall cannot be negative. Hence, the height of wall is 12 ft.  

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