Respuesta :
Answer:
l = 5
w = 16
OR
l = 16
w = 5
Step-by-step explanation:
p=2l+2w
A=l*w
42=2l+2w
divide by 2
21=l+w
solve for either l or w (I'll solve for l)
21-w=l
plug in l to area equation
80= (21-w)*w
80=21w-w²
bring the right side to the left side of the equation
w²-21w+80=0
find the zeros
w=5,16
plug w into the equation to find l
21-5=16
21-16=5
l=5,16
l = 5
w = 16
OR
l = 16
w = 5
A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. The length of the rectangle is 16cm, while the width of the rectangle is 5cm.
What is a rectangle?
A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.
Let the length of the rectangle be represented by L, while the width of the rectangle is represented by W.
Given the perimeter of the rectangle is 42 cm. Therefore, we can write,
42cm = 2(L + W)
21 = L + W
L = 21 - W
The area of the rectangle is 80 cm², therefore,
L × W = 80
(21 - W) × W = 80
W² - 21W + 80 = 0
[tex]W_{1,\:2}=\frac{-\left(-21\right)\pm \sqrt{\left(-21\right)^2-4\cdot \:1\cdot \:80}}{2\cdot \:1}[/tex]
W = 16, 5
Hence, the length of the rectangle is 16cm, while the width of the rectangle is 5cm.
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