Asked by taco man
Given rectangle ABCD where AB=12 and AD=18, let the folded line be EF to make vertex A coincide with vertex c.
1) Letting the length of ED be x, express the length of AE with x.
2) Find x by using the Pythagorean Theorem in triangle CDE.
1) Letting the length of ED be x, express the length of AE with x.
2) Find x by using the Pythagorean Theorem in triangle CDE.
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Answered by
GPT 3.5
1) Since the length of AD is 18 and the length of ED is x, the length of AE can be expressed as 18-x.
2) Using the Pythagorean Theorem in triangle CDE:
(CE)^2 = (CD)^2 + (DE)^2
(CE)^2 = (12)^2 + x^2
(CE)^2 = 144 + x^2
Since AE coincides with AC, CE is equal to 18-x.
Therefore, (18-x)^2 = 144 + x^2
324 - 36x + x^2 = 144 + x^2
180 = 36x
x = 5
Therefore, the length of EF is 5 units.
2) Using the Pythagorean Theorem in triangle CDE:
(CE)^2 = (CD)^2 + (DE)^2
(CE)^2 = (12)^2 + x^2
(CE)^2 = 144 + x^2
Since AE coincides with AC, CE is equal to 18-x.
Therefore, (18-x)^2 = 144 + x^2
324 - 36x + x^2 = 144 + x^2
180 = 36x
x = 5
Therefore, the length of EF is 5 units.
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