SOLUTION: A rectangle has base length x + 11, altitude length x + 7, and diagonals of length 4x each. What are the lengths of its base, altitude, and diagonals?

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Question 1193675: A rectangle has base length
x + 11,
altitude length
x + 7,
and diagonals of length
4x
each. What are the lengths of its base, altitude, and diagonals?
Found 2 solutions by greenestamps, Solver92311:
Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


The base, altitude, and diagonal form a right triangle with legs x+11 and x+7 and hypotenuse 4x. Use the Pythagorean Theorem to find x and answer the questions.

%28x%2B11%29%5E2%2B%28x%2B7%29%5E2=%284x%29%5E2
x%5E2%2B22x%2B121%2Bx%5E2%2B14x%2B49=16x%5E2
2x%5E2%2B36x%2B170=16x%5E2
14x%5E2-36x-170=0
7x%5E2-18x-85=0
%28x-5%29%287x%2B17%29=0

x = 5 or x=-17/7

Obviously the negative answer makes no sense in the problem, so x=5.

ANSWERS:
base = x+11 = 16
altitude = x+7=12
diagonal = 4x = 20

Answer by Solver92311(821) About Me  (Show Source):
You can put this solution on YOUR website!


The base, altitude, and diagonal of a rectangle form a right triangle with the diagonal as the hypotenuse. Use Pythagoras:



Simplify to a quadratic equation and solve either by factoring or the quadratic formula. Since you will find that this is a quadratic with a lead coefficient of opposite sign to the constant term, you are guaranteed two real solutions. If one of them is negative you can discard that solution because a negative value for would mean that the diagonal had a negative measure -- an absurd result.

Once you have the positive root of the equation, calculate , , and to obtain the measures of the desired line segments.

John

My calculator said it, I believe it, that settles it

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