Respuesta :
Given:
Let l denote the length of the rectangle.
Let w denote the width of the rectangle.
The length of a rectangle is 7 more than the width. This can be written in expression as,
[tex]l=7+w[/tex]
The area of the rectangle is 198 square centimeters.
We need to determine the length and width of the rectangle.
Length and width of the rectangle:
The length and width of the rectangle can be determined using the formula,
[tex]A=length \times width[/tex]
Substituting the values, we have;
[tex]198=(7+w)w[/tex]
Multiplying, we get;
[tex]198=7w+w^2[/tex]
[tex]0=7w+w^2-198[/tex]
Switch sides, we have;
[tex]w^2+7w-198=0[/tex]
Solving using the quadratic formula, we get;
[tex]w=\frac{-7 \pm \sqrt{(-7)^2-4(1)(-198)}}{2(1)}[/tex]
[tex]w=\frac{-7 \pm \sqrt{49+792}}{2}[/tex]
[tex]w=\frac{-7 \pm \sqrt{841}}{2}[/tex]
[tex]w=\frac{-7 \pm 29}{2}[/tex]
[tex]w=\frac{-7 +29}{2} \ or \ w=\frac{-7 -29}{2}[/tex]
[tex]w=\frac{22}{2} \ or \ w=\frac{-36}{2}[/tex]
[tex]w=11 \ or \ w=-18[/tex]
Since, the value of w cannot be negative, thus, w = 11
Thus, the width of the rectangle is 11 cm.
Substituting w = 11 in the equation [tex]l=7+w[/tex], we get;
[tex]l=7+11[/tex]
[tex]l=18[/tex]
Thus, the length of the rectangle is 18 cm.
Hence, the length and width of the rectangle are 18 cm and 11 cm respectively.
Answer:
he length of a rectangle is 7 more than the width.The area is 800 square centimeters. Find the length and width of the rectangle
Step-by-step explanation:
