A Senior Four student is allocated a rectangular piece of land for a project. The area of the plot is 12 m2. If the length of the plot is x+8m and width xm, form an equation for the area and factorise the equation to obtain the dimensions of the land.

Mathematics
A Senior Four student is allocated a rectangular piece of land for a project. The area of the plot is 12 m2. If the length of the plot is x+8m and width xm, form an equation for the area and factorise the equation to obtain the dimensions of the land.

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Answer

x2=12x^{2} = 12

Step 1: The area AA of a rectangular plot is given by the formula
A=length×width.A = length \times width.

Step 2: Given length = xx m and width = xx m, with area = 1212 m²,
substitute into the formula:
x m×x m=12 m2.x~m \times x~m = 12~m^2.

Step 3: Simplify the equation:
x2 m2=12 m2.x^2~m^2 = 12~m^2.
Divide both sides by m²:
x2=12.x^2 = 12.

The equation for the area factor is x2=12x^2 = 12.
x^{2 = 12}

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The area A of a rectangular plot is given by the formula A = length × width. Step 2: Given length = x m and width = x m, with area = 12 m², substitute into the formula: x~m × x~m = 12~m^2.

A Senior Four student is allocated a rectangular piece of land for a project. The area of the plot is 12 m2. If the length of the plot is x+8m and width xm, form an equation for the area and factorise the equation to obtain the dimensions of the land.
Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI Answer
Step 1: The area A of a rectangular plot is given by the formula A = length × width. Step 2: Given length = x m and width = x m, with area = 12 m², substitute into the formula: x~m × x~m = 12~m^2. Step 3: Simplify the equation: x^2~m^2 = 12~m^2. Divide both sides by m²: x^2 = 12. The equation for the area factor is x^2 = 12. x^2 = 12