The length of a rectangle is 5 m less than twice the width, and the area of the rectangle is 52 m^2. Find the dimensions of the rectangle.
Mathematics · Middle School · Tue Nov 03 2020
Answered on
Given:
Area of rectangle = 52 m^2
Length = w - 5
Width = w
Formula for the area of the rectangle:
A = lw
Solution:
Substitute the given area then the representation for length and width.
A = lw
52 = (w -5)w
52 = w^2 - 5w
w^2 - 5w - 52
a = 1
b = -5
c = -52
In order to find for w, we will use the quadratic equation.
The Quadratic formula:
w= −b ± √(b^2 − 4ac)/2a
is used to solve quadratic equations where a ≠ 0, in the form
ax^2+bx+c=0
When b^2−4ac=0 there is one real root.
When b^2−4ac>0 there are two real roots.
When b^2−4ac<0 there are no real roots, only a complex number.
w= −b ± √(b^2 − 4ac)/2a
w= −(-5) ± √((-5)^2 − 4(1)(-52))/2(1)
w= 5 ± √(25 +208)/2
w= 5 ± √(233)/2
w= 5 ± 15.266/2
Since width cannot be negative then we will only focus on +.
w = 5 + 15.266/2
w = 20.266/2
w = 10.13m
l = 10.13 - 5
l = 5.13m
Final answer:
w = 10.13
l = 5.13m