Isosceles trapezoid ABCD has legs AB and CD and base BC If AB = 7y – 4, BC = 4y – 6, and CD = 8y – 18, find the value of y.
The key here is "isosceles". That means the legs are equal.
7y-4 = 8y-18
y = 14
We are told that the legs of the isosceles trapezoid are AB and CD
AB = 7y - 4
CD = 8y - 18
In any isosceles trapezoid, the two legs are of
equal length. Therefore, AB = CD
7y - 4 = 8y - 18
Add 18 to both sides of the equation 7y - 4 + 18 = 8y - 18 + 18
7y + 14 = 8y
Subtract 7y from both sides of the equation
7y - 7y + 14 = 8y - 7y 14 = y
⇒y=14
Lmk if anything is wrong or nah
ummm......... is this right?
Its right
but what about the other one 4y-6? yall only be doing the sides and it wants y but you left out the base
You right fam thank you sm
To find the value of y, we need to use the properties of an isosceles trapezoid. One property of an isosceles trapezoid is that the legs (AB and CD in this case) are congruent.
Therefore, we can set up an equation by equating the lengths of AB and CD:
AB = CD
Substituting the given expressions for AB and CD:
7y – 4 = 8y – 18
To solve for y, we need to isolate the y term on one side of the equation. Let's do this step by step:
7y - 8y = -18 + 4
- y = -14
To get the value of y, we need to isolate it by multiplying by -1 on both sides:
(-1)(-y) = (-1)(-14)
y = 14
Therefore, the value of y is 14.