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

a. write and expression that represents the side length of the coaster.
answer: (d+4)

b. write an expression for the perimeter of the coaster.
answer : ?
please help !!!

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kudzordzifrancis

ANSWER

a. d+4

b. 4d+16

EXPLANATION

The area of the square coaster is represented by:

[tex] {d}^{2} + 8d + 16[/tex]

We split the middle term to obtain,

[tex] {d}^{2} + 4d + 4d + 16[/tex]

We factor by grouping to get,

[tex]d(d + 4) + 4(d + 4)[/tex]

[tex](d + 4)(d + 4) = {(d + 4)}^{2} [/tex]

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

[tex]l = d + 4[/tex]

b) The perimeter of a square is given by

[tex]P=4l[/tex]

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

[tex]P=4(d + 4)[/tex]

Or

[tex]P=4d + 16[/tex]

adioabiola

The expression that represent the length of the coaster is (d + 4)

Area of a square = l²

Given:

Area of a square = d² + 8d + 16

solve the quadratic expression

  • Find two numbers whose sum is 8d and product is 16

  • The two numbers are 4 and 4

d² + 4d + 4d + 16

  • factorise

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

(d + 4) (d + 4)

Area of a square = l²

= length × length

Perimeter of a square = 4 × length

= 4 × (d + 4)

= 4d + 16

Therefore, the expression for the perimeter of the coaster is 4d + 16

Learn more about area of a square:

https://brainly.com/question/24487155

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