If the diagonal of a rectangle is 25 cm and the length is 3cm more than triple the width what are the dimensions

625 = w^2 + (3w+3)^2 = w^2 + 9(w+1)^2 = w^2+9w^2+18w+9

625 = 10 w^2 + 18 w + 9
10 w^2 + 18 w - 616 = 0
5 w^2 + 9 w - 308 = 0
https://www.mathsisfun.com/quadratic-equation-solver.html
w = 7 (or - 8.8 :)
L = 21 + 3

width --- x

length -- 3x + 3

x^2 + (3x+3)^2 = 25^2
x^2 + 9x^2 + 18x + 9 - 625 = 0
10x^2 + 18x - 616 = 0

solve the quadratic using your favourite method
make sure to reject the negative and only use the positive answer

recognize the familiar 7-24-25 right triangle?

To find the dimensions of the rectangle, we can set up a system of equations.

Let's assume the width of the rectangle is x cm.

According to the given information, the length of the rectangle is 3 cm more than triple the width. Therefore, the length will be (3x + 3) cm.

We also know that the diagonal of the rectangle is 25 cm.

Using the Pythagorean theorem, we can relate the length, width, and diagonal of the rectangle:

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

Replacing the variables with the given values, we have:

25^2 = (3x + 3)^2 + x^2

Simplifying this equation, we get:

625 = 9x^2 + 18x + 9 + x^2

Combine like terms:

625 = 10x^2 + 18x + 9

Rearranging and setting the equation to zero:

10x^2 + 18x - 616 = 0

To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. In this case, let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 10, b = 18, and c = -616. Substituting these values into the quadratic formula, we get:

x = (-18 ± √(18^2 - 4*10*(-616))) / (2*10)

Simplifying further, we have:

x = (-18 ± √(324 + 24640)) / 20

x = (-18 ± √24964) / 20

Now, we can calculate the two possible values of x:

x1 = (-18 + √24964) / 20
x2 = (-18 - √24964) / 20

Evaluating these equations, we obtain:

x1 ≈ 4.57 cm
x2 ≈ -13.57 cm

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

Therefore, the width of the rectangle is approximately 4.57 cm.

Now, we can find the length using the earlier expression:

Length = 3x + 3
Length ≈ 3(4.57) + 3
Length ≈ 13.71 + 3
Length ≈ 16.71 cm

Hence, the dimensions of the rectangle are approximately 4.57 cm by 16.71 cm.