book Maths Puzzle Numerical Ability

a 15 foot ladder is placed against the wall of a house such that the botton of the ladder is at a distance of 10 feet from the wall. at what height does the ladder touch the house?

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Give the coordinates of a point on a coordinate grid that is a distance of the square root of 5 from point 1,3. Is there a formula to find the answer and how do you work out this problem?
Thank you Max Z = 5x1 + 6x2
subject to: 17x1 + 8x2 <= 136
3x1 + 4x2 <= 36
x1, x2 >= 0 and interger
What is the optimal soulition? Z =? Put the answer in the form xx with no additional nu