ABCD is an isosceles trapezoid with legs AB and CD. and with base BC. If AB=6z-5 and BC=7z+4 and CD=4z+3.
Find Z
Find BC
Z = 4
BC = 32
To find the value of z, we need to set up an equation using the given information about the lengths of AB, BC, and CD in the isosceles trapezoid.
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.
since AB ≅ CD,
6z-5 = 4z+3
solve for z and use that to find |BC|