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The painting shown at the right has an area of 240in^2. What is the value of​ x?

The painting shown at the right has an area of 240in^2. What is the value of​ x?-example-1
User Jsonbourne
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1 Answer

2 votes

Answer:

6.115 inches.

Explanation:

We know that the area of a rectangle is given by the formula:

Area = length x width

Here, the length is given by x inches and the width is given by 4x + 3 inches.

So, we can write:

Area = x(4x + 3)

Given that the area of the rectangle is 240 sq in, we can write:

240 = x(4x + 3)

Simplifying this equation, we get:

4x^2 + 3x - 240 = 0

We can solve for x by factoring the quadratic equation, or by using the quadratic formula.

Using the quadratic formula, we get:

x = (-3 ± sqrt(3^2 - 4(4)(-240))) / (2(4))

x = (-3 ± sqrt(2913)) / 8

x = (-3 ± 53.92) / 8

x = -8.865 or x = 6.115

Since the length of a side cannot be negative, we reject the negative solution.

Therefore, the value of x is approximately 6.115 inches.

User Sevensilvers
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7.1k points