the length of a rectangle is 6 cm more than its width. the area is 11 cm squared. find the length and width.
look at the post by anonymous at 8:55, it is almost the same as yours.
Do it the same way.
length= x+6
width=x
x(x+6)=11
x^2 + ^x =11
x^2+6x-11=0
(x-_)(x-_)
solve for x.
Then substute the x for the length and width.
To solve the equation x^2 + 6x - 11 = 0, we can use the quadratic formula.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
From the equation x^2 + 6x - 11 = 0, we can see that a = 1, b = 6, and c = -11.
Substituting these values into the quadratic formula, we have:
x = (-(6) ± √((6)^2 - 4(1)(-11))) / (2(1))
Simplifying further:
x = (-6 ± √(36 + 44)) / 2
x = (-6 ± √80) / 2
x = (-6 ± 8.944) / 2
Now, we can calculate the two possible values for x:
x₁ = (-6 + 8.944) / 2 ≈ 1.472
x₂ = (-6 - 8.944) / 2 ≈ -7.472
Since the dimensions of a rectangle cannot be negative, we can disregard x₂ = -7.472.
Therefore, the width of the rectangle, x, is approximately 1.472 cm.
To find the length, we can substitute this value back into the equation:
Length = x + 6 ≈ 1.472 + 6 ≈ 7.472 cm.
Therefore, the width of the rectangle is approximately 1.472 cm, and the length is approximately 7.472 cm.
To find the length and width of the rectangle, we need to solve the quadratic equation x^2 + 6x - 11 = 0, where x represents the width of the rectangle.
To solve the quadratic equation, we can use the quadratic formula: x = (-b ± sqrt(b^2 - 4ac))/(2a).
From the equation x^2 + 6x - 11 = 0, we know that a = 1, b = 6, and c = -11. Substituting these values into the quadratic formula, we get:
x = (-6 ± sqrt(6^2 - 4(1)(-11))) / (2(1))
x = (-6 ± sqrt(36 + 44)) / 2
x = (-6 ± sqrt(80)) / 2
x = (-6 ± 8.94) / 2
Simplifying further, we have:
x = (8.94 - 6) / 2 or x = (-8.94 - 6) / 2
x = 1.94 / 2 or x = -14.94 / 2
x = 0.97 or x = -7.47
Since length and width cannot be negative, we discard the solution x = -7.47.
Thus, the width of the rectangle is x = 0.97 cm.
Now, we can use the length-formula given in the problem: length = x + 6.
Substituting the width, we get: length = 0.97 + 6 = 6.97 cm.
Therefore, the length of the rectangle is 6.97 cm and the width is 0.97 cm.