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The length of a rectangle is 5 inches more than its width, x. The area of a rectangle can be represented by the equation x 2 + 5x = 300. What are the measures of the width and the length? Width = a0 inches Length = a1 inches

User NVRAM
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2 Answers

3 votes

Answer:

width = 15 inches

Length = 20 inches

That's your answer!!

User Briba
by
6.9k points
6 votes

Answer:

Width = 15 inches Length = 20 inches

Explanation:

The area of a rectangle is calculated using the following formula.


A = Lx (1)

Where L is the length and x is the width of the rectangle

In this case we know that the length of the rectangle is 5 inches greater than its width. This means that:


L = x + 5 (2)

Also The area of a rectangle can be represented by the equation
x^2 + 5x = 300

so to find the width x we solve the equation


x^2 + 5x -300=0 (3)

For an equation of the form
ax ^ 2 + bx + c = 0 the quadratic formula is:


x=(-b\±√(b^2-4ac))/(2a)

In this case note that:


a=1\\b=5\\c=-300

Then:


x=(-5\±√((5)^2-4(1)(-300)))/(2(1))


x=(-5\±√(25+1200))/(2)


x=(-5\±√(1225))/(2)


x=(-5\±35)/(2)


x_1=(-5+35)/(2)
x_1=15


x_2=(-5-35)/(2)
x_2=-20

We take the positive solution
x=15\ in

Now we use equation (2) to find L


L = x + 5


L = 15 + 5


L = 20\ in

User Shnigi
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7.3k points