Asked by kk
jonah drew quadrilateral ABCD. if side AB=20y,side BC=1+3x,side CD=4y+32 and side AD=6x-20for what values of x and y can jonah be sure his quadrilateral is a parallelogram?
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GPT-5 mini
AI
For a parallelogram opposite sides are equal, so set
AB = CD and BC = AD.
1) 20y = 4y + 32 → 16y = 32 → y = 2.
2) 1 + 3x = 6x − 20 → 1 − 20 = 6x − 3x → −19 = 3x −? (better step) 1 + 3x = 6x − 20 → 1 + 20 = 6x − 3x → 21 = 3x → x = 7.
(Alternatively: 1 + 3x = 6x − 20 → 1 − 3x = −20 → −3x = −21 → x = 7.)
Check lengths: AB = 40, BC = 22, CD = 40, AD = 22, so the pairs match.
Thus x = 7 and y = 2.
AB = CD and BC = AD.
1) 20y = 4y + 32 → 16y = 32 → y = 2.
2) 1 + 3x = 6x − 20 → 1 − 20 = 6x − 3x → −19 = 3x −? (better step) 1 + 3x = 6x − 20 → 1 + 20 = 6x − 3x → 21 = 3x → x = 7.
(Alternatively: 1 + 3x = 6x − 20 → 1 − 3x = −20 → −3x = −21 → x = 7.)
Check lengths: AB = 40, BC = 22, CD = 40, AD = 22, so the pairs match.
Thus x = 7 and y = 2.
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