lorenlizzeth
Answered

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Complete the work to find the dimensions of the rectangle. x(x – 3) = 10 x2 – 3x = 10 x2 – 3x – 10 = 10 – 10 (x + 2)(x – 5) = 0 What are the width and length of the rectangle?

Sagot :

MrRoyal

Answer:

[tex]Length =5[/tex]

[tex]Width = 2[/tex]

Step-by-step explanation:

Given

[tex]Length =x[/tex]

[tex]Width = x -3[/tex]

[tex]Area = 10[/tex]

[tex]x(x-3) =10[/tex]

See comment for missing part of the question

Required

Complete the expression to determine the dimension of a rectangle

We have:

[tex]x(x-3) =10[/tex]

Open bracket

[tex]x^2 -3x = 10[/tex]

Equate to 0

[tex]x^2 -3x - 10 =0[/tex]

Expand

[tex]x^2 + 2x - 5x - 10 = 0[/tex]

Factorize

[tex]x(x + 2) - 5(x + 2) = 0[/tex]

Factor out x + 2

[tex](x - 5)(x + 2) = 0[/tex]

Solve for x

[tex]x - 5 = 0[/tex] or [tex]x + 2 = 0[/tex]

[tex]x = 5[/tex] or [tex]x = -2[/tex]

The value of x cannot be negative

So:

[tex]x = 5[/tex]

Recall that:

[tex]Length = x[/tex]

[tex]Width = x - 3[/tex]

So:

[tex]Length =5[/tex]

[tex]Width = 2[/tex] ---- i.e. 5 - 3

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