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A large square is divided into 4 small congruent rectangles and a small square as shown. The areas of the large and small squares are 25 and 7, respectively. What is the length of a diagonal of a small rectangle?
+128474 The length of the side of the large square = 5 units
The length of the side of the small square = √7 units
The length of the shorter side of a rectangle = [ 5 - √7] / 2
The length of the longer side of the rectangle = 5 - [ 5 - √7 ] / 2 = [ 5 + √7]/ 2
So.....the squared length of the rectangle's diagonal =
( [ 5 - √7] / 2 )^2 + ( [ 5 + √7] / 2 )^2 =
[ 25 - 10√7 + 7 ] / 4 + [ 25 + 10√7 + 7 ] / 4 =
[ 64 / 4 ] =
16
So......the diagonal length = √16 = 4 units
