Question

A garden contains two square peanut beds. Find the length of each bed if the sum of the areas is 689ft^2 and difference of the areas is 111ft^2.

Answer 1

Given:

Sum of Areas of the square = 689 ft²

Difference of the Areas of the square = 111 ft²

Let's find the length of each bed.

From this situation, we have the set of equations:

A1 + A2 = 689

A1 - A2 = 111

Let l² represent the area of the first bed

Let m² represent the area of the second square bed

Thus, we have:

l² + m² = 689......................equation 1

l² - m² = 111..........................equation 2

Let's solve for l and m using substitution method.

rewrite equation 2 for l²:

Add m² to both sides

l² - m² + m² = 111 + m²

l² = 111 + m²

Substitute (111 + m²) for l² in equation 1:

l² + m² = 689

(111 + m²) + m² = 689

111 + m² + m² = 689

111 + 2m² = 689

Subtract 111 from both sides:

111 - 111 + 2m² = 689 - 111

2m² = 578

Divide both sides by 2:

`\begin{gathered} (2m^2)/(2)=(578)/(2) \\ \\ m^(2)=289 \end{gathered}`

Take the square root of both sides:

`\begin{gathered} \sqrt[]{m^2}=\sqrt[]{289} \\ \\ m=17 \end{gathered}`

Substitute 17 for m in either of the equations.

Let's take equation 2:

l² - m² = 111

l² - (17)² = 111

l² - 289 = 111

Add 289 to both sides:

l² - 289 + 289 = 111 + 289

l² = 400

Take the square root of both sides:

`\begin{gathered} \sqrt[]{l^2}=\sqrt[]{400} \\ \\ l=20 \end{gathered}`

Thus, we have the solutions:

l = 20, m = 17

The length of the first square peanut bed is 20 ft

The length of the second square peanut bed is 17 ft

ANSWER:

20 ft and 17 ft