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A piece of cardboard has the dimensions (x + 15) inches by (x) inches with the area of 60 in 2 . Write the quadratic equation that represents this and show your work. Then find the possible value(s) for x, and find the actual dimensions of the postcard.

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Answer:


x^2 + 15x - 60 = 0

The actual dimension is 18.28 by 3.28

Explanation:

Given

Dimension:


(x + 15)\ by\ x


Area = 60in^2

Required

Determine the quadratic equation and get the possible values of x

Solving (a): Quadratic Equation.

The cardboard is rectangular in shape.

Hence, Area is calculated as thus:


Area = Length * Width


60= (x + 15) * x

Open Bracket


60= x^2 + 15x

Subtract 60 from both sides


x^2 + 15x - 60 = 0

Hence, the above represents the quadratic equation

Solving (b): The actual dimension

First, we need to solve for x

This can be solved using quadratic formula:


x = (-b \± √(b^2 - 4ac))/(2a)

Where


a = 1


b = 15


c = -60

So:


x = (-b \± √(b^2 - 4ac))/(2a)


x = (-15 \± √(15^2 - 4*1*-60))/(2*1)


x = (-15 \± √(225 + 240))/(2)


x = (-15 \± √(465))/(2)


x = (-15 \± \21.56)/(2)

Split:


x = (-15 + 21.56)/(2) or
x = (-15 - 21.56)/(2)


x = (6.56)/(2) or
x = (-36.36)/(2)


x = 3.28 or
x = -18.18

But length can't be negative;

So:


x = 3.28

The actual dimensions:
(x + 15)\ by\ x is


Length =3.28 +15


Length =18.28


Width = x


Width =3.28

The actual dimension is 18.28 by 3.28

User Matilda Smeds
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