A 13foot ladder is leaning against a house The distance from

A 13-foot ladder is leaning against a house. The distance from the bottom of the ladder to the house is 7 feet less than the distance from the top of the ladder to the ground. How far is the bottom of the ladder from the house.

Solution

The ladder ,house form a right angled triangle.

ladder ----- hypotenuse ( 13 foot)

Height of house or top of the ladder to the ground ----height of triangle

Let it be h

distance between bottom of ladder and house ----- base

base = h-7

So, Applying pythagoras theorem:

13^2 = h^2 + (h-7)^2

169 = 2h^2 +49 -14h

2h^2 -14h - 120 =0

h^2 -7h -60 =0

h^2 -12h +5h -60 =0

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

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

h = -5 and h=12

We would neglect the -ve value

So, h= 12 foot

Bottom of ladder from house =h-7 = 12-7 = 5 foot