Answer:
side length of the smaller room = 5 m
Side length of the larger room = 8 m
Step-by-step explanation:
Total area of two square room = 89 m²
Area of a square = side²
Let
x = side of the smaller square
x + 3 = side of the longer square
Total area = area of room A + Area of room B
89 = x² + (x + 3)²
89 = x² + x² + 6x + 9
89 - 9 = 2x² + 6x
2x² + 6x = 80
2x² + 6x - 80 = 0
Divide through by 2
x² + 3x - 40 = 0
Solve quadratic equation using factorization method
x² + 8x - 5x - 40 = 0
x(x + 8) -5(x + 8) = 0
(x - 5) (x + 8) = 0
(x - 5) = 0 (x + 8) = 0
x = 5 x = -8
The side length of a square room can not be a negative value
Therefore, side length of the smaller room = 5 m
Side length of the larger room = 5 + 3
= 8 m
