Question

A school is installing a flagpole in the central plaza. The plaza is a square with side length 100 yards as shown in the figure below. The flagpole will take up a square plot in the middle of the plaza and its base will have an area of x2−10x+25 yd2. Area of the flagpole plot: x2−10x+25 A plaza square with a small flagpole square in the middle. 100 yards100 yards Find the length of the base of the flagpole by factoring. (Hint: Because the area of the flagpole is an expression that involves the variable x, the length of the base will also involve the variable x.) The length of the base of the flagpole is

Answer 1

The area of the flagpole is:

`x^2-10x+25`

This represents a perfect square, because it can be represented as below:

`x^2-2\cdot5+5^2`

Therefore we can use the notable product, square of the difference to factor the expression:

`(x-5)^2=(x-5)\cdot(x-5)`

Since the area of the flagpole is the product between it's length and width, then we know that the length and width are equal and are equivalent to:

`\text{length}=\text{width}=(x-5)`