The area of a rectangle is 72 cm². The length. l, of the rectangle is 6 cm longer than the width, w.
What is the width of the rectangle?
10 cm
8 cm
6 cm
2 cm
Area = l*w
So let width be w and length be w+6
Noe equation is
B(B+6) = 72
Solve for B and find the answer
width ---- w
length ---- w+6
width*length = area
w(w+6) = 72
w^2 + 6w - 72 = 0
(w-6)(w+12) = 0
w = 6 or w = a negative
the width is 6 cm
with only a few nice choices you could have easily checked each one in your head
e.g.
for the first one: is 10 times 16 equal to 72 ? NO
etc
6cm
If the rectangle measure 72cm²and it's width is 6cm , identify it's length
To find the width of the rectangle, we need to set up an equation based on the given information.
Let's assume the width of the rectangle is w. According to the problem, the length l is 6 cm longer than the width, so we can write the equation:
l = w + 6
The formula for the area of a rectangle is:
Area = length × width
Substituting the given values, we have:
72 = (w + 6) × w
Now, we can solve this equation for w by simplifying and rearranging:
72 = w² + 6w
0 = w² + 6w - 72
To solve this quadratic equation, we can factor or use the quadratic formula. In this case, since the equation can be factored, we'll do that:
0 = (w + 12)(w - 6)
Setting each factor equal to zero and solving for w, we have:
w + 12 = 0 or w - 6 = 0
w = -12 or w = 6
Since the width of a rectangle cannot be negative, we discard w = -12. Therefore, the width of the rectangle is 6 cm.
Therefore, the correct answer is: 6 cm