Respuesta :
P = 2(L + W)
56 = 2(L + W)
56/2 = L + W
28 = L + W.....L = 28 - W
A = L * W
132 = W(28 - W)
132 = -W^2 + 28W
W^2 - 28W + 132 = 0
(W - 6)(W - 22) = 0
W - 6 = 0 L = 28 - W
W = 6 L = 28 - 6
L = 22
W - 22 = 0 L = 28 - W
W = 22 L = 28 - 22
L = 6
not sure which (length or width)....one of them is 6 ft and the other is 22 ft
56 = 2(L + W)
56/2 = L + W
28 = L + W.....L = 28 - W
A = L * W
132 = W(28 - W)
132 = -W^2 + 28W
W^2 - 28W + 132 = 0
(W - 6)(W - 22) = 0
W - 6 = 0 L = 28 - W
W = 6 L = 28 - 6
L = 22
W - 22 = 0 L = 28 - W
W = 22 L = 28 - 22
L = 6
not sure which (length or width)....one of them is 6 ft and the other is 22 ft
The possible lengths of sides of the rectangle will be [tex](6,22)[/tex] or [tex](22,6)[/tex] .
What is area ?
Area is the space which is occupied by any [tex]2D[/tex] surface.
Area of rectangle [tex]=Length\ *\ Breadth[/tex]
Perimeter of rectangle [tex]=2(Length\ +\ Breadth)[/tex]
We have,
Perimeter of rectangle [tex]=56[/tex] feet
Area of rectangle [tex]=132[/tex] squared feet
Let,
Length of rectangle [tex]=x[/tex]
Breadth of rectangle [tex]=y[/tex]
So,
Perimeter of rectangle [tex]=2(Length\ +\ Breadth)[/tex]
[tex]56=2(x+y)[/tex]
[tex]28=(x+y)[/tex]
⇒ [tex]x=28-y[/tex] [tex]........(i)[/tex]
Now,
Area of rectangle [tex]=Length\ *\ Breadth[/tex]
[tex]132=x\ *\ y[/tex] [tex]........(ii)[/tex]
Now substitute value of [tex]x[/tex] in [tex](ii)[/tex],
[tex]132=(28-y)y[/tex]
[tex]132=28y-y^2[/tex]
⇒[tex]y^2-28y+132=0[/tex]
Now using Middle term split method;
[tex]y^2-28y+132=0[/tex]
[tex]y^2-22y-6y+132=0[/tex]
[tex]y(y-22)-6(y-22)=0[/tex]
[tex](y-6)(y-22)=0[/tex]
⇒
[tex](y-6)=0[/tex]
⇒ [tex]y=6[/tex]
[tex](y-22)=0[/tex]
⇒ [tex]y=22[/tex]
So,
Now if we take [tex]y=6[/tex], then
[tex]x=28-6[/tex]
[tex]x=22[/tex]
And,
if we take [tex]y=22[/tex], then
[tex]x=28-22[/tex]
[tex]x=6[/tex]
So, the possible lengths of sides of the rectangle are [tex](6,22)[/tex] or [tex](22,6)[/tex] .
Hence, we can say that he possible lengths of sides of the rectangle are [tex](6,22)[/tex] or [tex](22,6)[/tex] .
To know more about rectangle click here
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