They rectangular courtyard has a cement walkway around its perimeter the dimensions of the courtyard are shown in the diagram. Write an expression in factored form that represents the areas of the cement walkway. Outside rectangle is 3 yards x 3 yards inside rectangle is(5x/1)yd and 21yd
3*3 - (5x/1)(21)
I suspect a typo. why have a denominator of 1?
and how can an inside rectangle have a length of 21 when the outside has a length of only 3?
To find the area of the cement walkway, we need to subtract the area of the inside rectangle from the area of the outside rectangle.
The area of the outside rectangle is given by the formula: length * width
In this case, the length of the outside rectangle is 3 yards and the width is 3 yards. Therefore, the area of the outside rectangle is:
3 * 3 = 9 square yards
The area of the inside rectangle is also given by the formula: length * width
In this case, the length of the inside rectangle is (5x/1) yards and the width is 21 yards. Therefore, the area of the inside rectangle is:
(5x/1) * 21 = 105x square yards
To find the area of the cement walkway, we subtract the area of the inside rectangle from the area of the outside rectangle:
Area of cement walkway = Area of outside rectangle - Area of inside rectangle
= 9 square yards - 105x square yards
So the expression in factored form that represents the areas of the cement walkway is:
9 - 105x square yards
To find the area of the cement walkway, we need to subtract the area of the inner rectangle from the area of the outer rectangle.
The area of the outer rectangle is given by the product of its length and width. In this case, the length is 3 yards and the width is 3 yards. So, the area of the outer rectangle is 3 * 3 = 9 square yards.
The area of the inner rectangle is also given by the product of its length and width. In this case, the length is (5x/1) yards and the width is 21 yards. So, the area of the inner rectangle is (5x/1) * 21 = 105x square yards.
To find the area of the cement walkway, we subtract the area of the inner rectangle from the area of the outer rectangle:
9 - 105x = -105x + 9
Therefore, the expression in factored form that represents the area of the cement walkway is (-105x + 9) square yards.