Question
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.
Answers
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.