The diagonal of a rectangle is 26 inches long. Its length is 14 inches more than the height. What is the height of the rectangle?

You can use the Pythagorean equation (a^2 + b^2= c^2 ) because the triangle the diagonal and the 2 sides make is a right triangle.

H= height of rectangle
14+H= width of rectangle

H^2 + (14+H)^2 = 26^2

Solve for h to find height:)

Well, well, well, we have a rectangle with a diagonal strutting its stuff at 26 inches. Impressive!

Now, according to my calculations, the diagonal, the length, and the height of the rectangle form a right triangle. It's like a geometry party going on!

Using the Pythagorean theorem, we can let the height be "x" inches. And since the length is 14 inches more than the height, we can write it as "x + 14" inches.

So, according to the theorem, we have x^2 + (x + 14)^2 = 26^2.

Now, let's solve this equation and find out the height of our rectangle! Math, ho!

Calculating, calculating...

After a few chuckles and number crunching, I found the height to be approximately 8.25 inches.

So, the height of the rectangle is about 8.25 inches. Keep it up, Mr. Rectangle!

To find the height of the rectangle, let's set up an equation using the given information.

Let's assume the height of the rectangle is represented by 'h' inches. Since the length of the rectangle is 14 inches more than the height, we can say that the length is 'h + 14' inches.

We are also given that the diagonal of the rectangle is 26 inches. In a rectangle, the diagonal, height, and length form a right triangle. We can use the Pythagorean theorem to relate the diagonal, height, and length:

(diagonal)^2 = (height)^2 + (length)^2

Substituting the given values into the equation, we get:

26^2 = h^2 + (h + 14)^2

Simplifying this equation:

676 = h^2 + (h^2 + 28h + 196)

Combining like terms:

2h^2 + 28h + 196 - 676 = 0

2h^2 + 28h - 480 = 0

Dividing both sides by 2 to simplify the equation:

h^2 + 14h - 240 = 0

Now we have a quadratic equation. We can solve for 'h' by factoring, completing the square, or using the quadratic formula. Let's solve it by factoring:

(h - 8)(h + 30) = 0

Setting each factor equal to zero:

h - 8 = 0 or h + 30 = 0

Solving for 'h' in each equation:

h = 8 or h = -30

Since the height of a rectangle cannot be negative, we discard the value of -30. Therefore, the height of the rectangle is 8 inches.