Question

The area (in square centimeters) of a square coaster can be represented by d^2+8d+16 .

Answer 1

ANSWER

a. d+4

b. 4d+16

EXPLANATION

The area of the square coaster is represented by:

${d}^{2} + 8d + 16$

We split the middle term to obtain,

${d}^{2} + 4d + 4d + 16$

We factor by grouping to get,

$d(d + 4) + 4(d + 4)$

$(d + 4)(d + 4) = {(d + 4)}^{2}$

Since area of a square is l² , it means the side length of the square is

$l = d + 4$

b) The perimeter of a square is given by

$P=4l$

We substitute the length in terms of d, to obtain;

$P=4(d + 4)$

Or

$P=4d + 16$

Answer 2

Answer :

(a) The expression that represents the side length of the coaster is, $Side=(d+4)$

(b) The expression that represents the perimeter of the coaster is, $Perimeter=4d+16$

Step-by-step explanation :

As we are given that the area of a square coaster can be represented by:

$d^2+8d+16$

Now we are simplifying this expression by middle term splitting method.

$d^2+8d+16$

$=d^2+4d+4d+16$

$=d(d+4)+4(d+4)$

$=(d+4)(d+4)$

$=(d+4)^2$

Part (a) :

As, the area of a square is (side)², this means the side length of the square is:

$Side=(d+4)$

Part (b) :

The perimeter of square is, 4(side)

That means,

$Perimeter=4(d+4)=4d+16$