Given Isosceles trapezoid ABCD. AB = 3x - 4 and CD = x + 12. Find AB.
Isosceles trapezoid A B C D is drawn.
2
8
16
20
AB = 3X - 4.
CD = X + 12.
The non-parallel sides of an isosceles trapezoid are equal:
AB = CD,
3X - 4 = X + 12,
3X - X = 12 - 4,
2X = 8,
X = 4.
AB = 3X - 4 = 3 * 4 - 4 = 8.
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To find the length of AB in the isosceles trapezoid ABCD, we can set up an equation using the given information.
AB = 3x - 4
CD = x + 12
Since ABCD is an isosceles trapezoid, the bases AB and CD are parallel and have equal lengths.
AB = CD
So, we can set up the equation:
3x - 4 = x + 12
To solve for x, we can subtract x from both sides of the equation:
3x - x - 4 = x - x + 12
2x - 4 = 12
Next, we can add 4 to both sides:
2x - 4 + 4 = 12 + 4
2x = 16
Finally, we can divide both sides by 2 to isolate x:
(2x)/2 = 16/2
x = 8
Now, we substitute the value of x back into the equation for AB:
AB = 3x - 4
AB = 3(8) - 4
AB = 24 - 4
AB = 20
Therefore, AB is equal to 20.
To find the length of AB in the isosceles trapezoid, we can use the fact that opposite sides of an isosceles trapezoid are parallel. In this case, AB || CD.
Since AB and CD are parallel sides of the trapezoid, we can subtract their lengths to find the distance between them:
CD - AB = x + 12 - (3x - 4)
Simplifying, we get:
CD - AB = x + 12 - 3x + 4
= -2x + 16
Since AB and CD are equal in an isosceles trapezoid, we can set this equal to zero:
-2x + 16 = 0
Solving for x, we find:
-2x = -16
x = -16 / -2
x = 8
Now that we have the value of x, we can substitute it back into either AB = 3x - 4 or CD = x + 12. Let's use AB = 3x - 4:
AB = 3(8) - 4
= 24 - 4
= 20
Therefore, the length of AB is 20.