since AB ≅ CD,
6z-5 = 4z+3
solve for z and use that to find |BC|
Find Z
Find BC
6z-5 = 4z+3
solve for z and use that to find |BC|
BC = 32
In an isosceles trapezoid, the legs (AB and CD) are congruent. This means their lengths are equal. So, we can set up an equation:
AB = CD
According to the given information:
AB = 6z - 5
CD = 4z + 3
Now, we can set up the equation and solve for z:
6z - 5 = 4z + 3
To solve this equation, we need to isolate the variable z on one side of the equation. Let's do that:
6z - 4z = 3 + 5
2z = 8
Finally, we solve for z by dividing both sides of the equation by 2:
z = 8 / 2
z = 4
So, the value of z is 4.
Now, let's find the length of BC. According to the given information, BC is equal to 7z + 4.
Substituting the value of z we found earlier (z = 4) into the equation:
BC = 7(4) + 4
BC = 28 + 4
BC = 32
Therefore, the length of BC is 32.