10 foot ladder and a 2

Question

a 10 ft ladder is leaning against a building in such a away that the distance from the building to the base of the ladder is 2 ft less than the distance from the base of building on the top of the ladder. How high uptrend building wall does does the ladder reach

Answer 1

b^2 + h^2 = 10^2

b=h-2

(h-2)^2 + h^2 = 100

h^2 -4h + 4 + h^2 =100

2h^2 -4h -96 =0

h^2 -2h - 48 = 0

(h-8)(h+6) = 0 set the factors =0 and solve for h. ignore the negative length

h= 8 feet high from the top of the ladder to the ground level, bottom of the building

b= 8-2 = 6 feet from the ladder to the building on the ground

Answer 2

Let x ft be the distance from building base to ladder along the ground is (x-2) ft

Using Pythagoras gives x^2 + (x-2)^2 =10^2

simplifies to x^2 -2x -48 =0

giving (x-8)(x+6) = 0

so x = 8 or -6

x=-6 ft is extraneous solution thus

x= 8 ft is the answer