The length of a rectangle mat was 1¹/²m longer than it's width.find the length of the mat if it's area is 4½m²
Let the width of the mat be "x" meters.
According to the given information, the length of the mat is 1¹/²m longer than its width.
So, the length of the mat is "x + 1¹/²" meters.
The formula for the area of a rectangle is given by:
Area = Length x Width
Substituting the given values into the formula, we have:
4½m² = (x + 1¹/²) * x
Simplifying this equation, we get:
4½m² = x² + 1¹/²x
To solve for x, we need to convert 4½m² to an improper fraction:
4½m² = 9/2 m²
So, the equation becomes:
9/2 m² = x² + 1¹/²x
Multiplying the equation by 2 to eliminate the denominator, we have:
9 m² = 2x² + 3x
Rearranging this equation, we get:
2x² + 3x - 9 = 0
To solve this quadratic equation, we can either factorize it, complete the square, or use the quadratic formula.
Factoring it, we have:
(2x - 3)(x + 3) = 0
Setting each factor equal to zero, we get:
2x - 3 = 0 or x + 3 = 0
Solving these equations, we find:
2x = 3 or x = -3
Dividing both sides of the equation 2x = 3 by 2, we get:
x = 3/2
Therefore, the width of the mat is 3/2 meters.
Substituting this value back into the equation for the length of the mat, we have:
Length = x + 1¹/²
Length = (3/2) + 1¹/²
Length = (3/2) + (3/2)
Length = 6/2
Length = 3 meters
Therefore, the length of the mat is 3 meters.