Assuming segments from A to E and from B to D to be straight, find BC.
If the shape looks like a cricket bowtie, the #s are AB=10, BC=3x-2, DE=6 CD=x+2
angles B(top left corner)& D(bottom right corner)are 90* angles
To find BC, we need to use the information given about the lengths and angles in the shape.
First, let's consider the right triangle BCD. From the given information, we know that angle BCD is a 90-degree angle and the length of CD is x + 2.
Next, let's consider the right triangle BAC. We know that AB has a length of 10, and the angle BAC is also a 90-degree angle.
Since AB and AC are straight and connected, we can combine the information from both triangles to find the length of BC.
Using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides, we can set up the equation:
(BC)^2 = (AB)^2 + (AC)^2
Substituting the given lengths, we have:
(3x - 2)^2 = 10^2 + (x + 2)^2
Expanding and simplifying the equation:
9x^2 - 12x + 4 = 100 + x^2 + 4x + 4
Combining like terms:
8x^2 - 16x - 96 = 0
Dividing both sides by 8:
x^2 - 2x - 12 = 0
Factoring or using the quadratic formula, we find that x = 4 or x = -3.
Since length cannot be negative in this context, we take x = 4.
Now we can substitute x = 4 back into the given expression for BC:
BC = 3x - 2
BC = 3(4) - 2
BC = 12 - 2
BC = 10
Therefore, BC has a length of 10.