Questions on Geometry: Pythagorean theorem answered by real tutors!

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Question 132521: If the area of a square is 169 square centimeters, what is the length of the diagnal?
: If the area of a square is 169 square centimeters, what is the length of the diagnal?

Answer by elima(1420) About Me  (Show Source):
You can put this solution on YOUR website!
If the area of a square is 169 square centimeters, what is the length of the diagnal?
formula for area of square;
a=s^2
169=s^2
take the square root of each side;
sqrt(169)=sqrt(s^2)
13=s
so the sides of the square are 13, now we can use Pythagoreans thereom to find the diagonal;
a^2 + b^2 = c^2
13^2 + 13^2 = c^2
26^2 = c^2
take square root of each side;
sqrt(26^2) = sqrt(c^2)
26 = c
so diagonal = 26
:)
Question 132521: If the area of a square is 169 square centimeters, what is the length of the diagnal?
: If the area of a square is 169 square centimeters, what is the length of the diagnal?

Answer by solver91311(1850) About Me  (Show Source):
You can put this solution on YOUR website!
The length of a side of a square given the area is given by the square root of the area. So this square has a side length of sqrt(169)=13

The diagonal of any square forms an isoceles right triangle with two of the sides of the square, and the three sides of this triangle are in proportion 1:1:sqrt(2) (verify this yourself by considering an isoceles right triangle with legs that measure 1 unit, then applying the Pythagorean Theorem). Knowing that, all we need to do is multiply the side length times sqrt(2), in this case: 13sqrt(2) cm is the length of the diagonal of a square with an area of 169cm^2.