find the width of a rectangle with a diagonal and lenght of 20cm and 15cm respectively?
w^2 + 15^2 = 20^2 ----- simple Pythagoras
w^2 + 225 = 400
etc
a rectangle is 5cm longer than it is wide. the diagonal of the rectangle is 20 cm. determine the dimensions of the rectangle. explain and show your work
To find the width of a rectangle when given the diagonal and length, you can use the Pythagorean theorem. The Pythagorean theorem states that for any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the diagonal of the rectangle forms the hypotenuse of a right triangle, while the length and width of the rectangle form the other two sides. Let's denote the width of the rectangle as "w".
Using the Pythagorean theorem, we can set up the equation:
w^2 + 15^2 = 20^2
Simplifying, we have:
w^2 + 225 = 400
Subtracting 225 from both sides:
w^2 = 175
To find the width, we take the square root of both sides:
w = √175
Using a calculator, we can find that the square root of 175 is approximately 13.23.
Therefore, the width of the rectangle is approximately 13.23 cm.