Question

A garden contains two square peanut beds. Find the length of each bed if the sum of the areas is 769 ft2 and the difference of the areas is 481 ft2.

Answer 1

lengths are 25 ft and 12 ft

Explanation:

let x and y be the areas of the 2 square peanut beds, with x being greater than y , then

x + y = 769 → (1)

x - y = 481 → (2)

add (1) and (2) term by term to eliminate y

(x + x) + (y - y) = 769 + 481

2x + 0 = 1250

2x = 1250 ( divide both sides by 2 )

x = 625

substitute x = 625 into (1) and solve for y

625 + y = 769 ( subtract 625 from both sides )

y = 144

the areas of the 2 beds are 625 ft² and 144 ft²

the area (A) of a square is calculated as

A = s² ( s is the length of side )

then

s² = 625 ( take square root of both sides )

s =
`√(625)` = 25

and

s² = 144 ( take square root of both sides )

s =
`√(144)` = 12

length of each bed is 25 ft and 12 ft