Question

Help me find the value of Y!

ABCD is an isosceles trapezoid with legs AB and CD and base BC. If the length of AB is 7y-4, the length of BC is 4y-6, and the length of CD is 8y-18, find the value of y.
I know 2 lengths are equal and I know algebra but I just don't know where to start. Please explain it. Sorry there's no diagram

Answer 1

Answer: y = 14

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Step-by-step explanation:

You are correct in thinking you'll set two things equal to one another. This type of thing happens often in algebra. The question you probably have is: what two things do I set equal?

The key term is "isosceles" which tells us we have two non-parallel sides equal in this trapezoid. In other words, we ignore the parallel sides.

The non-parallel sides of a trapezoid are known as the legs.

The legs in this case are

• AB = 7y-4
• CD = 8y-18

Set those expressions equal to one another and solve for the variable y.

AB = CD

7y-4 = 8y-18

-4+18 = 8y-7y

14 = y

y = 14 is the final answer

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Check:

• AB = 7y-4 = 7*14-4 = 98-4 = 94
• CD = 8y-18 = 8*14-18 = 112-18 = 94

Both legs AB and CD are 94 units long to confirm this trapezoid is indeed isosceles. The answer is confirmed.

Side note: as mentioned earlier, we completely ignore BC = 4y-6. It was probably put in there as a distraction.