Question

ABCD is quadrilateral where the opposite sides are equal suppose AB=x and BC=2x-3

Evaluate x so that ABCD is a rhombus

Answer 1

To determine the value of x for ABCD to be a rhombus, given that AB=x and BC=2x-3, we set x equal to 2x-3 and solve for x, finding that x must equal 3.

Step-by-step explanation:

To evaluate x so that ABCD is a rhombus, we must remember that in a rhombus all sides are equal. Given that AB=x and BC=2x-3, for ABCD to be a rhombus, AB must be equal to BC.

Setting the two expressions equal to each other because all sides must be the same in a rhombus:

x = 2x - 3

We then solve for x by subtracting x from both sides:

0 = x - 3

Adding 3 to both sides, we get:

x = 3

Therefore, x must equal 3 for quadrilateral ABCD to be a rhombus.