SOLUTION: in radical form what is the length of a diagonal of a sqaure if the perimeter is 20

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: in radical form what is the length of a diagonal of a sqaure if the perimeter is 20      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 528501: in radical form what is the length of a diagonal of a sqaure if the perimeter is 20
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
The diagonal of a square defines two congruent right triangles.
The diagonal is the hypotenuse.
The Pythagorean Theorem teaches us:
.
+c%5E2+=+a%5E2+%2B+b%5E2+
.
With a square, a=b so we have
.
+c%5E2+=+2a%5E2+
.
+c+=+sqrt%282a%5E2%29+=+a%2Asqrt%282%29+
.
We are told perimeter = 20, which for a square = 4*a
.
+a+=+5+
.
Substitute a=5
.
+c+=+5%2Asqrt%282%29+=+7.071067811865476+
.
Check this proposed answer to make sure it is correct.
.
+7.071067811865476%5E2+=+2%2A5%5E2+ ??
.
+7.071067811865476%5E2+=+50+
.
+2%2A5%5E2+=+2%2A25+=+50+
.
Correct.