Answer:
71 & 25 m
Explanation:
a • b = 1775
2a + 2b = 192
substitution:
a = 1775/b
2(1775/b) + 2b = 192
distribute the 2
(3550/b) + 2b = 192
subtract 192 from both sides
(3550/b) + 2b - 192 = 0
transform the expression by dividing all terms by b
(3550 + 2b² - 192b) / b = 0
when the quotient of expressions equals 0, the numerator has to be 0
3550 + 2b² - 192b = 0
reorder the terms
2b² - 192 b + 3550 = 0
divide by sides by 2
b² - 96b + 1775 = 0
rewrite -96b as a difference using factoring X
b² - 25b - 71b + 1775 = 0
factor the expression (factor out b)
b (b-25) - 71b + 1775
factor out b - 25 from the expression
(b - 25) (b - 71) = 0
if b = 25 or 71, then a = 71 or 25
71 & 25 m