jim owns a square piece of land with a side length of a meters. he extends his property by purchasing adjacent land so that the length is increased by 10 m and the width by 12 m. write an algebraic expression for the area of jim's extended property
old property = lw
new property = (l+10)(w+12)
L+10 w+12
To find the area of Jim's extended property, we need to calculate the area of the original square piece of land and add the additional area created by extending the length and width.
Let's start by finding the area of the original square with a side length of a meters. The formula for the area of a square is given by the equation: Area = side length × side length. Therefore, the area of the original square is a × a, or a^2.
Next, we consider the additional area created by extending the length by 10 meters and the width by 12 meters. Since the original square only had one side length, we need to determine the new length and width after the extension.
After extending the length by 10 meters, the new length becomes (a + 10) meters. Similarly, after extending the width by 12 meters, the new width becomes (a + 12) meters.
The formula for the area of a rectangle is given by the equation: Area = length × width. Therefore, the additional area created is (a + 10) × (a + 12).
To find the total area of Jim's extended property, we add the area of the original square to the additional area: a^2 + (a + 10) × (a + 12).
Hence, the algebraic expression for the area of Jim's extended property is a^2 + (a + 10) × (a + 12).