The answer is 80 square meters.
The square area is expressed as:
A = a²,
where A is the area of the square, and a is the side of the square.
The rectangle area is expressed as:
A₁ = a₁ · b₁,
where A₁ is the area of the rectangle, and a₁ and b₁ are the sides of the rectangle.
After renovations, square garden becomes rectangular.
One side is doubled in length:
a₁ = 2a
The other side is decreased by three meters.
b₁ = a - 3
The new area is 25% than the original square garden:
A₁ = A + 25%A =
= A + 25/100·A
= A + 1/25·A
= a² + 1/25·a²
= <span>a² + 0.25·a²
</span> = 1.25·a²
If the starting equation is:
A₁ = a₁ · b₁
Thus, the equation is:
1.25a² = 2a·(<span>a - 3)
</span>1.25a² = 2a · a - 2a · 3
1.25a² = 2a² - 6a
<span>Therefore, the equation that could be used to determine the length of a side of the original square garden is:
</span><u>2a² - 6a = </u><span><u>1.25a²</u></span>
Now, we will solve the equation:
2a² - 6a = 1.25a²
2a² - 1.25a² - 6a = 0
0.75a² - 6a = 0
⇒ a(0.75a - 6) = 0
From here, one of the multiplier must be zero - either a or (0.75a - 6). Since a could not be zero, (0.75a - 6) is:
0.75a - 6 = 0
0.75a = 6
a = 6 ÷ 0.75
a = 8
If the side of the square is 8, then the area of the rectangle is
A₁ = 1.25 · a²
A₁ = 1.25 ·8²
A₁ = 1.25 · 64
A₁ = 80
Therefore, the area of the new rectangle garden is 80 square meters.
Let us say that h is the height of the guardrail.
Therefore the inequality equation that we can generate from this scenario is:
| h – 106 | = ± 7
There are two ways to solve this, either the equation is
positive or negative.
When the equation is positive, therefore:
| h – 106 | = 7
h = 7 + 106 = 113 cm
When the equation is negative, therefore:
| h – 106 | = - 7
h = -7 + 106 = 99 cm
So the height must be 99 cm to 113 cm
Patio area = backyard area - pool area
= 7x10 - (pi)2^2 = 57.43 sq.cm
1cm = 3ft ; 1 sqcm = 9 sq.ft
patio area = 57.43x9 = 516.87
answer is b
[decimal difference us due to value of pi ]
