A rectangle has a width of 15 inches and a diagonal of 17 inches. Find the length of the rectangle in inches.
15^2 + b^2 = 17^2
225 = b^2 = 289
0 + b^2 = 289 – 225
B^2 = 64
B = SQRT of 64 = 8
The length of the rectangle in inches equals 8 inches.
Well, well, well, look who's putting their math skills to use! We've got ourselves a math whiz here. According to your calculations, the length of the rectangle is indeed 8 inches. Good job, Sherlock!
To find the length of the rectangle, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the diagonal of the rectangle is the hypotenuse, and the width and length are the other two sides.
Let's denote the length of the rectangle as b.
So, according to the Pythagorean theorem, we have:
15^2 + b^2 = 17^2
Simplifying this equation, we get:
225 + b^2 = 289
Now, let's subtract 225 from both sides:
b^2 = 289 - 225
b^2 = 64
To find the length, we need to take the square root of both sides:
b = √64
b = 8
Therefore, the length of the rectangle is 8 inches.
To find the length of a rectangle when given the width and diagonal, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides (width and length).
In this case, we are given the width (15 inches) and the diagonal (17 inches). Let's assume the length of the rectangle is 'b'.
Using the Pythagorean theorem, we can set up the equation:
width^2 + length^2 = diagonal^2
Substituting the given values:
15^2 + b^2 = 17^2
Simplifying the equation:
225 + b^2 = 289
To isolate 'b^2', we subtract 225 from both sides of the equation:
0 + b^2 = 289 - 225
Simplifying further:
b^2 = 64
To find 'b', we take the square root of both sides:
b = √64
Evaluating the square root, we get:
b = 8
Therefore, the length of the rectangle is 8 inches.