SOLUTION: Carpenters and builders will sometimes measure 3 ft from a corner along one wall and 4 ft along the other, then check that it's 5 ft between the 2 points. If it is, the walls are "

Question 199738: Carpenters and builders will sometimes measure 3 ft from a corner along one wall and 4 ft along the other, then check that it's 5 ft between the 2 points. If it is, the walls are "square", at right angles.
If the two short sides of a building are 3 and 4 how would you show carefully that you used the Pythagorean theorem to calculate the diagonal as 5?

Found 2 solutions by jerrybassmasta, tutor_paul:
Answer by jerrybassmasta(14) (Show Source): You can put this solution on YOUR website!
So solve your question, you must first find out the formula for Pythagorean Theorem.
The formula for that is a^2+b^2=c^2.
A and B being the legs.(3,4)
C being the hypotenuse. (in your case 5)
So plug in the numbers into the formula and then solve.
3^2+4^2=c^2
9+16=c^2
25=c^2
the square root of 25 = c^2
5=c
Therefore, you proved that the distance between those two walls are 5 feet
To check your answer just plug in the 5 into the formula.
3^2+4^2=25
9+16=25
25=25
Answer by tutor_paul(519) (Show Source): You can put this solution on YOUR website!
The Pythagorean Theorem is wriiten as follows:

Where:
a = one side of a right triangle
b = the other side of a right triangle
c = the hypoteneuse (diagonal) of a right trianagle
.
Note that this equation applies only to right triangles - which is a triangle which has one angle of 90 degrees. The hypoteneuse is the side of the triangle opposite this 90 degree angle.
.
So back to the problem... the goal is to make sure that the walls of the building are "square." That means that they form a 90 degree angle. So let's apply the pythagorean theorem to prove that if the 2 walls are length 3 and 4 respectively, the diagonal is 5.
.
Pythagorean Theorem:

Substitute in your given values:

Simplify:

So you have proven that the diagonal is 5. Thus from the given information in the problem, you also know that the walls form a right angle.
============
Good Luck,
tutor_paul@yahoo.com

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