A rectangular blacktop with a length of 5x and a width of 3x has been erected inside a rectangular field that has a length of 12x and a width of 7x. what is the area of the part of the field that is not blacktop.

Question

wio · Answer

Can you draw it?

wio · Answer

|dw:1709090096015:dw|
This is my interpretation.

wio · Answer

Area of a rectangle is:$$
\text{Area}_{\text{rectangle}} = \text{length} \times \text{width}
$$Thus we have:
$$
\text{Area}_{\text{blacktop}}  = 5\times 3
$$and$$
\text{Area}_{\text{field}}  = 12\times 7
$$

wio · Answer

They want you to find:$$
\text{Area}_\text{field} -\text{Area}_\text{blacktop} = (12\times 7) - (5\times 3)
$$

Conqueror99 · Answer

@wio wrote:

Area of a rectangle is:$$ \text{Area}_{\text{rectangle}} = \text{length} \times \text{width} $$Thus we have: $$ \text{Area}_{\text{blacktop}} = 5\times 3 $$and$$ \text{Area}_{\text{field}} = 12\times 7 $$

Nice

toga · Answer

To find the area of the part of the field that is not blacktop, we first need to calculate the area of the blacktop.

The area of the blacktop is the product of its length and width, which is:

5x * 3x = 15x^2

Now, to find the area of the part of the field that is not blacktop, we need to subtract the area of the blacktop from the area of the entire field.

The area of the entire field is the product of its length and width, which is:

12x * 7x = 84x^2

So, the area of the part of the field that is not blacktop is:

84x^2 - 15x^2 = 69x^2

Therefore, the area of the part of the field that is not blacktop is 69x^2.