SOLUTION: Find the dimensions of a rectangle if the area equals 100 and the proportion is 4:3. Hello I am puzzled by this question but I think I have a start.I tried setting up a equation su

Algebra ->  Rectangles -> SOLUTION: Find the dimensions of a rectangle if the area equals 100 and the proportion is 4:3. Hello I am puzzled by this question but I think I have a start.I tried setting up a equation su      Log On


   

Question 625527: Find the dimensions of a rectangle if the area equals 100 and the proportion is 4:3. Hello I am puzzled by this question but I think I have a start.I tried setting up a equation such that (3k)(4k)=100.
If anybody could help me by guiding me to correct way to solve this type of problem I would greatly appreciate it THANKS
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The straightforward way is:
Let +L+ = length
Let +W+ = width
given:
Area = +100+
(1) +L%2AW+=+100+
(2) +L%2FW+=+4%2F3+
---------------
Multiply both sides of (2) by +3W+
(2) +3L+=+4W+
(2) +L+=+%284%2F3%29%2AW+
Plug this result into (1)
(1) +%284%2F3%29%2AW%2AW+=+100+
(1) +%284%2F3%29%2AW%5E2=+100+
(1) +W%5E2+=+%283%2F4%29%2A100+
(1) +W%5E2+=+75+
(1) +W+=+sqrt%2875%29+
(1) +W+=+5%2Asqrt%283%29+
and
(2) +L+=+%284%2F3%29%2AW+
(2) +L+=+%284%2F3%29%2A5%28+sqrt%283%29+%29+
(2) +L+=+%28+20%2Asqrt%283%29+%29+%2F+3+
check answers:
(1) +L%2AW+=+100+
(1) +%28%28+20%2Asqrt%283%29+%29+%2F+3+%29%2A%28+5%2Asqrt%283%29+%29+=+100+
(1) +sqrt%283%29+%2A+sqrt%283%29+%2A+%28+20++%2F+3+%29+%2A+5+=+100+
(1) +3%2A%28+100%2F3%29+=+100+
(1) +100+=+100+
and, also:
(2) +L%2FW+=+4%2F3+
(2) +%28%28+20%2Asqrt%283%29+%29+%2F+3%29+%2F+%285%2Asqrt%283%29%29+=+4%2F3+
(2) +%2820%2F3%29+%2F+5+=+4%2F3+
(2) +4%2F3+=+4%2F3+
OK