A rectangular parking lot is 20 ft longer than it is wide. Find the dimensions of the parking lot if it measures 100 ft diagonally

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To find the dimensions of the rectangular parking lot, we can use the Pythagorean theorem.

Let's denote the width of the parking lot as $$ w $$ and the length as $$ l $$.

Given that the parking lot is 20 ft longer than it is wide, we have the relationship:
$$ l = w + 20 $$

We are also given that the diagonal of the parking lot measures 100 ft. Using the Pythagorean theorem, we can write:
$$ w^2 + l^2 = 100^2 $$

Substitute $$ l = w + 20 $$ into the equation:
$$ w^2 + (w + 20)^2 = 100^2 $$

Now, we can solve this equation to find the dimensions of the parking lot.
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
  $$w^{2}+\left(w+20\right)^{2}=100^{2}$$
- step1: Expand the expression:
  $$2w^{2}+40w+400=10000$$
- step2: Move the expression to the left side:
  $$2w^{2}+40w-9600=0$$
- step3: Factor the expression:
  $$2\left(w-60\right)\left(w+80\right)=0$$
- step4: Divide the terms:
  $$\left(w-60\right)\left(w+80\right)=0$$
- step5: Separate into possible cases:
  $$\begin{align}&w-60=0\&w+80=0\end{align}$$
- step6: Solve the equation:
  $$\begin{align}&w=60\&w=-80\end{align}$$
- step7: Rewrite:
  $$w_{1}=-80,w_{2}=60$$
The solutions to the equation are $$ w = -80 $$ and $$ w = 60 $$.

Since the width of the parking lot cannot be negative, we discard the solution $$ w = -80 $$.

Therefore, the width of the parking lot is 60 ft, and the length is 60 + 20 = 80 ft.

The dimensions of the rectangular parking lot are 60 ft by 80 ft.
The dimensions of the parking lot are 60 ft by 80 ft.

A rectangular parking lot is 20 ft longer than it is wide. Find the dimensions of the parking lot if it measures 100 ft diagonally

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