Chapter 1.1, Problem 77E

Area of a Garden Mary’s backyard vegetable garden measures 20 ft by 30 ft, so its area is 20 × 30 = 600 ft². She decides to make it longer, as shown in the figure, so that the area increases to A = 20(30 + x). Which property of real numbers tells us that the new area can also be written A = 600 + 20x?

To determine

The property of real numbers, so that the new area can be written as $A=600+20x$.

Answer to Problem 77E

The property of real numbers that tells us that the new area can also be written as $A=600+20x$ is distributive property.

Explanation of Solution

Given:

The length of the vegetable garden is $30\text{ft}$.

The breadth of the vegetable garden is $20\text{ft}$.

The area of the garden is $600{\text{ft}}^2$.

The length of the garden is increased by $x$. The area of the garden is increased to $A=20\left(30+x\right)$.

Calculation:

The distributive property of real numbers states that multiplication of a number by a sum of two numbers is equivalent to the addition of the result obtained by multiplication of the number by each of the terms.

$a\left(b+c\right)=ab+ac$

The current are of the garden is $20\times 30=600\text{f}{t}^2$.

When the length of the garden is increased by x. The area of the garden is increased as follows.

$A=20\left(30+x\right)$

Use the distributive property of real numbers and find the area.

$\begin{array}{c}A=20\times 30+20\times x\\ =600+20x\end{array}$

The new area of the garden is already mentioned as $A=600+20x$.

Therefore, the property of real numbers that tells us that the new area can also be written as $A=600+20x$ is distributive property.