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2 years ago

The area of the rectangle to the right is 68 square feet

Mathematics

1 answer:

den301095 [7]2 years ago

6 0

Step-by-step explanation:

We know that

Area of the rectangle=Length×Breadth

➝(x+4)(x-9)=68

➝x(x-9)+4(x-9)=68

➝x^2-9x+4x+-32=68

➝x^2-5x-32=68

➝x^2-5x=68+32

➝x^2-5x=100

➝x^2-5x-100=0

The equation has no real roots hence this situation can't be possible

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Your family is installing a new square pool in the backyard. The existing patio has a side length of 8 feet. How much of the pat

trasher [3.6K]

The question is an illustration of perimeters.

The amount of patio to remove to install the pool is 8 feet.

From the question, we have:

$\mathbf{Length\ of\ the\ pool = 8}$

$\mathbf{Length\ of\ walkway = 1}$

The perimeter of the patio is:

$\mathbf{P_p = 4 \times Length\ of\ the\ pool}$

$\mathbf{P_p = 4 \times 8}$

$\mathbf{P_p = 32}$

A 1ft walkway means that;

1ft would be subtracted from both sides of the patio before installing the pool

So, the perimeter of the patio in terms of the length of the pool is:

$\mathbf{P_p = 4 \times (x +2)}$

Equate both expressions

$\mathbf{P_p = P_p}$

$\mathbf{4 \times (x +2) = 32}$

Divide both sides by 4

$\mathbf{x +2 = 8}$

Subtract 2 from both sides

$\mathbf{x = 6}$

So, the perimeter of the pool is:

$\mathbf{P_{pool} = 4 \times 6}$

$\mathbf{P_{pool} = 24}$

The amount of patio to remove is:

$\mathbf{Amount = P_p - P_{pool}}$

So, we have:

$\mathbf{Amount = 32 - 24}$

$\mathbf{Amount = 8}$

Hence, 8ft of the patio would be removed to install the pool

<em>See attachment for illustration</em>