The sides of a rectangular floor are ym and (y+7)m. The diagonal is (y+8)m ,calculate, in metres; the value of y,and the area of the floor
To find the value of y, we can use the Pythagorean theorem, which states that the square of the length of the diagonal is equal to the sum of the squares of the lengths of the two sides of a right-angled triangle.
Therefore, we have:
(y^2 + (y+7)^2 = (y+8)^2
Expanding and simplifying, we get:
y^2 + y^2 + 14y + 49 = y^2 + 16y + 64
Rearranging and simplifying further, we get:
2y^2 + 14y + 49 = y^2 + 16y + 64
Subtracting y^2 from both sides:
y^2 - 2y - 15 = 0
Factoring the quadratic equation, we get:
(y - 5)(y + 3) = 0
This gives us two possible values for y: y = 5 and y = -3.
Since the length of a side cannot be negative, the value of y is 5.
To calculate the area of the floor, we can use the formula for the area of a rectangle:
Area = length x width
Area = ym x (y+7)m
Area = 5m x (5+7)m
Area = 5m x 12m
Area = 60 square meters
Therefore, the value of y is 5 and the area of the floor is 60 square meters.