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kept on a stool

by sanju09 » Thu May 06, 2010 6:16 am
The length of a ladder is exactly equal to the height of the wall it is resting against. If lower end of the ladder is kept on a stool of height 3 and the stool is kept 9 away from the wall, the upper end of the ladder coincides with the top of the wall. What is the height of the wall?
(A) 11
(B) 12
(C) 15
(D) 18
(E) 21
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by liferocks » Thu May 06, 2010 6:30 am
ladder wall and distance of the stool from wall makes an right angled triangle where one side is 9

if its a 3,4,5 triangle then other sides will be 12 and 15

if the side of wall is 12 then total height of wall..include the stool height=length of ladder=15

Ans option C 15
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by Ashish8 » Thu May 06, 2010 7:26 am
Can someone verify if this method works. I got the same answer as liferocks, albeit it was negative.

The ladder is leaning on the wall and the floor and the wall make a right angle.

height of slanted ladder = a
Wall height = a + 3

pythagorean theorem:

9^2 + (a + 3)^2 = a^2 (FOIL)

81 + a^2 + 6a + 9 = a^2 (Subtract a^2)

81 + 6a + 9 = 0 (Subtract 90)

6a = -90

a = -15
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by liferocks » Thu May 06, 2010 7:40 am
Ashish8 wrote:Can someone verify if this method works. I got the same answer as liferocks, albeit it was negative.

The ladder is leaning on the wall and the floor and the wall make a right angle.

height of slanted ladder = a
Wall height = a + 3

pythagorean theorem:

9^2 + (a + 3)^2 = a^2 (FOIL)

81 + a^2 + 6a + 9 = a^2 (Subtract a^2)

81 + 6a + 9 = 0 (Subtract 90)

6a = -90

a = -15
just a small correction
wall height is a and from pythagororus theorem we get

9^2+(a-3)^2=a^2
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by kstv » Thu May 06, 2010 8:11 am
Image

h² = 9² + (h-3)²
6h = 90
h = 15
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