Question

Find a formula for the described function. A rectangle has perimeter 8 m. Express the area A of the rectangle as a function of the length, L, of one of its sides

Answer 1

Answer:

$A(L) = 4L - L^2$

Step-by-step explanation:

Given

Perimeter = 8m

Required

Determine its area as a function of length

Represent Length and Width with L and W, respectively;

Perimeter (P) is calculated as thus;

$P = 2(L + W)$

Substitute 8 for P

$8 = 2(L + W)$

Divide both sides by 2

$4 = L + W$

Make W the subject of formula

$W = 4 - L$

Area (A) of a rectangle is calculated as thus:

$A = L * W$

Substitute 4 - L for W

$A = L * (4 - L)$

Open bracket

$A = 4L - L^2$

Represent as a function

$A(L) = 4L - L^2$

Answer 2

Area of rectangle in terms of length L is

$A(L)= 4L-L^2$

Given :

A rectangle has perimeter 8 m. Express the area A of the rectangle as a function of the length, L, of one of its sides

We know that the perimeter of rectangle formula is

$perimeter = 2(length)+2(width )$

perimeter is 8m

Let the length of rectangle is L

$P=2L+2W\\8=2(L+W)\\4=L+W\\W=4-L$

so width is 4-L

Now we use area formula

Area of rectangle = length times width

$A=L(W)\\A=L(4-L)\\A= 4L-L^2$

Area of rectangle in terms of length L is

$A= 4L-L^2$

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