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The rectangle below has an area of x^2+11x+28x 2 +11x+28x, squared, plus, 11, x, plus, 28 square meters and a length of x+7x+7x, plus, 7 meters. What expression represents the width of the rectangle?

Respuesta :

MrRoyal

Answer:

[tex]Width = x + 4[/tex]

Step-by-step explanation:

Given

Shape: Rectangle

[tex]Area = x^2 + 11x + 28[/tex]

[tex]Length = x + 7[/tex]

Required

Determine the width

For a rectangle:

[tex]Area = Length * Width[/tex]

Substitute values for Length and Area

[tex]x^2 + 11x + 28 = (x + 7) * Width[/tex]

Factorize the expression on the left hand side

[tex]x^2 + 7x + 4x + 28 = (x + 7) * Width[/tex]

[tex]x(x + 7) + 4(x + 7) = (x + 7) * Width[/tex]

[tex](x + 7)(x + 4) = (x + 7) * Width[/tex]

Divide both sides by x + 7

[tex]Width = x + 4[/tex]

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