Question
The two of us ordered a pizza whose area was the same as the area of a square in which the sum of the squares of the four sides plus the sum of the squares of the two diagonals is 400. The pizza's area was
A. 50
B. 100
C. 150
D. 200
A. 50
B. 100
C. 150
D. 200
Answers
Reiny
let the side of the square be x
let d be the diagonal,
d^2 = x^2+x^2 = 2x^2
d = √2 x
"the sum of the squares of the four sides plus the sum of the squares of the two diagonals is 400"
x^2+x^2+x^2+x^2 + 2(2x^2) = 400
8x^2 = 400
x^2 = 50
x = 5√2
area of square pizza is x^2
= 50
let d be the diagonal,
d^2 = x^2+x^2 = 2x^2
d = √2 x
"the sum of the squares of the four sides plus the sum of the squares of the two diagonals is 400"
x^2+x^2+x^2+x^2 + 2(2x^2) = 400
8x^2 = 400
x^2 = 50
x = 5√2
area of square pizza is x^2
= 50