Solving a system of equations, we will see that the length is 3cm and the width is 10cm.
How to find the length and width of the rectangle?
For a rectangle of length L and width W, the perimeter is:
P = 2*(W + L)
And the area is:
A = L*W
Here we know that the area is 30 centimeters squared, and the perimeter is 26 centimeters, then we can replace that in the two equations above so we get:
26cm = 2*(W + L)
30cm^2 = L*W
This is a system of equations, to solve this, we need to isolate one of the variables in one of the equations. I will isolate L on the first equation:
26cm = 2*(W + L)
26cm/2 - W = L
13cm - W = L
Now we can replace that in the area equation:
30cm^2 = (13cm - W)*W
Now we need to solve the quadratic equation:
30cm^2 = 13cm*W - W^2
-W^2 + 13cm*W - 30cm^2 = 0
The solutions are:
W = (-13cm ± √( (13cm)^2 - 4*(-30cm^2)*(-1))/(2*-1)
W = (-13cm ± 7cm)/-2
The positive solution is:
W = (-13cm - 7cm)/-2 = 10cm
Then the width is 10 cm, and the length is:
13cm - 10cm = L = 3mc
Then the rectangle is 10cm by 3cm.
If you want to learn more about rectangles:
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