Question

A field with an area of 2880 ft2 has the shape of a rectangle, whose length is 12 ft larger than its width. Find the dimensions of this field.

Answer 1

width is 48, length is 60

Explanation:

Answer 2

Answer: The dimensions of the field are

width = 40 ft and length = 60 ft.

Step-by-step explanation: Given that a field with an area of 2880 ft² has the shape of a rectangle with length 12 ft larger than the width.

We are to find the dimensions of the field.

Let w ft be the width of the given rectangular field.

Then, the length of the field will be (w + 12) ft.

According to the given information, we have

`w * (w+12)=2880\\\\\Rightarrow w^2+12w=2880\\\\\Rightarrow w^2+12w-2880=0\\\\\Rightarrow w^2+60w-48w-2880=0\\\\\Rightarrow w(w+60)-48(w+60)=0\\\\\Rightarrow (w-48)(w+60)=0\\\\\Rightarrow w-48=0,~~~w+60=0\\\\\Rightarrow w=48,-60.`

Since the measure of a side of a rectangle cannot be negative, so w = 48.

This implies that

length of the field = w + 12 = 48 + 12 = 60 ft.

Thus, the dimensions of the field are

width = 40 ft and length = 60 ft.