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Leviafan [203]
2 years ago
10

Given that a rectangle with length $3x$ inches and width $x + 5$ inches has the property that its area and perimeter have equal

values, what is $x$
Mathematics
2 answers:
nadezda [96]2 years ago
8 0

Answer:

\huge\boxed{x = 1 \ \ \ \ OR \ \ \ \ x = -\frac{10}{3} }

Step-by-step explanation:

Length = 3x

Width = x + 5

<u>Area of Rectangle:</u>

=> (Length)(Width)

=> (3x)(x+5)

=> 3x^2 + 15x

<u>Perimeter of Rectangle:</u>

=> 2 (Length) + 2 (Width)

=> 2(3x) + 2(x+5)

=> 6x + 2x + 10

=> 8x + 10

<u>Given Condition is:</u>

Perimeter = Area

3x^2 + 15x = 8x + 10

3x^2 + 15 x -8x - 10 = 0\\3x^2 + 7x -10 = 0\\3x^2 + 10 x - 3x -10 = 0\\x(3x+10) - 1(3x+10) = 0\\(x-1) (3x+10) = 0

<u><em>Either,</em></u>

x - 1 = 0       OR     3x + 10 = 0

x = 1             OR       3x = -10

x = 1             OR        x = -10 / 3

scoray [572]2 years ago
7 0

Answer:

First, we need to know how to calculate the area and the permiter of a rectangle.

To calculate the area, we multiply base by height and to calculate the perimeter, we sum all sides.

Knowing this, we can say that the area is 3x * (x+5) and the perimiter is 3x + 3x + x + 5 + x + 5, as we know both are the same, we write it as an equation:

3x * (x+5) = 3x + 3x + x + 5 + x + 5

Now we solve the equation:

3x^2 +15x = 6x + 2x + 10

3x^2+15x =8x + 10

3x^2+15x-8x-10=0

3x^2+7x-10=0\\\\x_1=\frac{-10}{3}\\x_2 = 1

As the negative result doesn't have sense, we only pick the second one: 1.

If x = 1, then area would be 3*6 = 18 square inches and perimeter 3+3+6+6 = 18 inches

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Answer:

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Step-by-step explanation:

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