one side of a square is lengthened by 4 feet and the other side is lengthened by 2 feet.the resulting rectangle has an area of 30 square feet. what are the dimensions of the original square?

Answer 1

answer: about 2.568 feet = side of the square

basic solution method as follows

(x+4)(x+2) = 30 ft^2

x^2 + 6x + 8 = 30

complete the square. add (6/2)^2=9 to both sides

take half the coefficient of the x term and square it to get 9

x^2 + 6x + 9 = 30+9

(x+3)^2 = 39

x+3= sqr39 (ignore the negative square root)

x = -3 + sqr39 feet = side length of the square

= about 3.245 feet

check the answer

(3.245 + 4)(3.245 +2)

= 7.245(5.245 = about 38, not 30, mistake(s)

check back for corrected calculations

trial & error

square's side = 3, 7x5 = 35 still too big

square's side = 2 6x4 = 24 too small

2.5 6.5x4.5 = 29 1/4 close still a tad to small

2.6 6.6 x4.6 = 30.36 closer but too big

2.568 6.568x4.5568= 30.003 ft^2 = 30 rounded to nearest 1/100th

original square had sides = about 2.568 feet each

figure out the mistake(s) in 1st method above and you win a big prize, a one way air line ticket, all expenses paid (except for baggage and the peanuts dinner) to the vacation paradise of Gaza or Russian held territory of the Ukraine. Your choice. Go for it