The diagonal of a rectangular room is 52 ft long. one wall measures 28 ft longer than the adjacent wall. Find the dimensions of the room.

x^2 + (x+28)^2 = 52^2

x^2 + x^2 + 56 x + 784 = 2704

2 x^2 + 56 x - 1920 = 0

x^2 + 28 x -960 = 0

x = [-28 +/- sqrt(28^2 + 3840) ]/2

x = [ 28 +/- 68 ]/2

x = 48
48 - 28 = 20

so 48 by 20

Well, well, well, looks like we have a perplexing puzzle here! Let's put on our thinking caps and solve this riddle.

Let the adjacent wall be x ft long. Since the other wall is 28 ft longer, we can say it's x + 28 ft long.

Now we can use the good ol' Pythagorean theorem. According to Mr. Pythagoras, the diagonal squared is equal to the sum of the squares of the other two sides. So we have:

(x^2) + ((x + 28)^2) = (52^2)

Now, let's expand and simplify this equation:

x^2 + (x^2 + 56x + 784) = 2704

Combine the like terms:

2x^2 + 56x + 784 = 2704

Subtract 2704 from both sides:

2x^2 + 56x - 1920 = 0

Now, let's solve this quadratic equation. If only life had an "easy" button for quadratic equations, right?

Using the quadratic formula, x = (-b ± √(b^2 - 4ac))/(2a), we can plug in the values:

x = (-56 ± √(56^2 - 4(2)(-1920)))/(2(2))

After some fancy footwork, we find two possible solutions: x = 20 and x = -48. But since we're dealing with the length of walls, we'll discard the negative value.

So, the adjacent wall measures 20 ft, and the other wall measures 20 + 28 = 48 ft.

Therefore, the dimensions of the room are 20 ft by 48 ft.

Voila! The mystery has been solved. Now, it's time to celebrate your math skills or treat yourself to a little clown-inspired joke. How about this one?

Why don't skeletons fight each other?

They don’t have the guts!

Let's assume the shorter side of the room as "x" ft.

As given, the longer side of the room is 28 ft longer than the adjacent wall, so it would be (x + 28) ft.

Using the Pythagorean theorem, the diagonal of the rectangular room can be found using the formula:

diagonal^2 = shorter side^2 + longer side^2

Substituting the values, we have:

52^2 = x^2 + (x + 28)^2

Simplifying the equation:

2704 = x^2 + x^2 + 56x + 784

Combining like terms:

2x^2 + 56x + 784 - 2704 = 0

2x^2 + 56x - 1920 = 0

Simplifying further by dividing the equation by 2:

x^2 + 28x - 960 = 0

Now we can solve this quadratic equation by factoring or using the quadratic formula.

Factoring the equation:

(x + 60)(x - 32) = 0

Setting each factor equal to zero:

x + 60 = 0 or x - 32 = 0

Solving for x:

x = -60 or x = 32

Since the dimensions cannot be negative, we discard the negative value.

Therefore, the shorter side of the room is 32 ft.

The longer side of the room can be found by adding 28 to the shorter side:

x + 28 = 32 + 28 = 60 ft

So the dimensions of the room are 32 ft by 60 ft.

To find the dimensions of the room, let's assign variables to the lengths of the two adjacent walls. Let's say the length of the shorter wall is x ft.

According to the problem, the longer wall measures 28 ft longer than the adjacent wall, so its length would be (x + 28) ft.

We can use the Pythagorean theorem to relate the lengths of the two adjacent walls and the diagonal of the room:

(diagonal)^2 = (adjacent wall 1)^2 + (adjacent wall 2)^2

Substituting the given values, we have:

52^2 = x^2 + (x + 28)^2

To solve for x, we need to simplify and solve the quadratic equation. Let's expand and rearrange the equation:

2704 = x^2 + (x^2 + 56x + 784)

Combine like terms:

2704 = 2x^2 + 56x + 784

Rearrange the equation to have a quadratic equation equal to zero:

2x^2 + 56x + 784 - 2704 = 0

Combine like terms:

2x^2 + 56x - 1920 = 0

Divide the equation through by 2 to simplify:

x^2 + 28x - 960 = 0

Now we can solve this quadratic equation. We can factor it or use the quadratic formula:

Lets try to factor:

(x + 60)(x - 16) = 0

From the zero product property, we have two possible solutions:

x + 60 = 0 or x - 16 = 0

Solving for x, we have two possible values:

x = -60 or x = 16

Since the length of a wall cannot be negative, we discard the negative solution. Therefore, x = 16 ft.

So the length of the shorter wall is 16 ft, and the longer wall is (16 + 28) = 44 ft.

Hence, the dimensions of the room are 16 ft by 44 ft.