Asked by raven
find the dimensions of a rectangle having perimeter 14m and diagonal of length 5m
Answers
Answered by
drwls
Let the diagonal be c and the sides a and b
b = sqrt (c^2 - a^2) = sqrt(25-a^2)
Perimeter = 2a + 2b = 2a + 2sqrt (25-a^2) = 14
14 - 2a = 2 sqrt (25-a^2)
196 - 56a + 4a^2 = 4(25-a^2) = 100 -4a^2
8a^2 -56a +96 = 0
a^2 -7a + 12 = 0
(a-3)(a-4) = 0
The side lengths are 3 and 4
b = sqrt (c^2 - a^2) = sqrt(25-a^2)
Perimeter = 2a + 2b = 2a + 2sqrt (25-a^2) = 14
14 - 2a = 2 sqrt (25-a^2)
196 - 56a + 4a^2 = 4(25-a^2) = 100 -4a^2
8a^2 -56a +96 = 0
a^2 -7a + 12 = 0
(a-3)(a-4) = 0
The side lengths are 3 and 4
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.