SOLUTION: The diagonal of a rectangle is √96. Its length is 9. Find the side of a square having the same area as that of the given rectangle

Algebra ->  Rectangles -> SOLUTION: The diagonal of a rectangle is √96. Its length is 9. Find the side of a square having the same area as that of the given rectangle      Log On


   

Question 936408: The diagonal of a rectangle is √96. Its length is 9. Find the side of a square having the same area as that of the given rectangle
Answer by srinivas.g(540) About Me  (Show Source):
You can put this solution on YOUR website!
diagonal of rectangle (d) =sqrt%2896%29
length(l)= 9
side (b)= ? (unknown )
as Pythagorean theorem
+diagonal%5E2+=length%5E2%2Bside%5E2
+%28sqrt%2896%29%29%5E2+=+9%5E2%2Bb%5E2
96+=+81%2Bb%5E2
move 81 to the left
+96-81+=b%5E2
15=b%5E2
apply square root on both sides, to get b
+sqrt%2815%29+=sqrt%28b%5E2%29
+sqrt%2815%29=+b
3.87 =b
width (b) =3.87
area of rectangle = length *side
= 9*3.87
=34.85
area of rectangle = area of square
let x be the side of square
area of square =x%5E2
+x%5E2=34.85
+x=sqrt%2834.85%29
+x=5.9
side of square = 5.9