a dining table in the shape of a rectangle ABCD has sides of length (2X+12)and x cm and the length of the diagonal BD is (2x+18)find the value of x

The is useless becoz u r nit telling properly that whats the answer

To find the value of x, we can use the properties of a rectangle.

In a rectangle, the length of the diagonal is equal to the square root of the sum of the squares of the lengths of the sides.

Given that the diagonal BD is (2x+18) cm, we can set up the equation:

(2x+18)^2 = (2x+12)^2 + x^2

Expanding both sides:

4x^2 + 36x + 324 = 4x^2 + 48x + 144 + x^2

Combining like terms:

4x^2 + 36x + 324 = 4x^2 + x^2 + 48x + 144

Simplifying:

3x^2 + 12x + 180 = 0

Dividing the equation by 3:

x^2 + 4x + 60 = 0

This is a quadratic equation, and we can solve it using factoring, completing the square, or using the quadratic formula. However, in this case, the equation can be factored as:

(x + 6)(x + 10) = 0

Setting each factor equal to zero:

x + 6 = 0 or x + 10 = 0

Solving for x:

x = -6 or x = -10

Since the length of a side cannot be negative, we can disregard -6 as a solution. Therefore, the value of x is x = -10.

However, it is important to note that negative values for x may not make sense in the context of the problem. Please double-check the given information or provide any additional information if necessary.

To find the value of x, we can use the Pythagorean theorem, which 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, we have a rectangle ABCD, and the diagonal BD is the hypotenuse of a right triangle with sides AB and AD.

Let's apply the Pythagorean theorem to the given information:

(2X + 12)^2 + x^2 = (2x + 18)^2

Expanding both sides of the equation:

4X^2 + 48X + 144 + x^2 = 4x^2 + 72x + 324

Rearranging and simplifying the equation:

4x^2 - x^2 + 72x - 48x = 324 - 144

3x^2 + 24x - 180 = 0

Now, we can solve this quadratic equation to find the value of x.

Either by factoring, completing the square, or using the quadratic formula, we simplify the equation and find the two possible values of x.

After finding the values of x, substitute them back into the original question to see if they satisfy the given condition that the length of the diagonal BD is (2x + 18).

we know that

(2x+12)^2 + x^2 = (2x+18)^2
expand all that and solve the quadratic, and you get

x = 30

check: 30^2 + 72^2 = 78^2
That's just 6 times a 5-12-13 triangle