SOLUTION: Easy Word Problem Two rectangles have the same area of 120m^2. the difference of their length 5m and their breadth is 4m find their sides Please solve it in manner like let......

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Easy Word Problem Two rectangles have the same area of 120m^2. the difference of their length 5m and their breadth is 4m find their sides Please solve it in manner like let......      Log On


   



Question 762860: Easy Word Problem
Two rectangles have the same area of 120m^2. the difference of their length 5m and their breadth is 4m find their sides
Please solve it in manner like let........be x
and let...........be y
Please Help Thank you in advance

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the rectangles r1 and r2
Call the breadth of r1 +x+
Call the length of r1 +y+
--------------------
The breadth of r2 = +x+%2B+4+
The length of r2 = ++y+-+5+
( if I made the signs the same, the area of r2
would be greater than the area of r1 )
---------------------------
(1) +120+=+x%2Ay+
(2) +120+=+%28+x%2B4+%29%2A%28+y+-5+%29+
--------------------------
(2) +x%2Ay+%2B+4y+-+5x+-+20+=+120+
(2) +x%2Ay+%2B+4y+-+5x+=+140+
-------------------------
(1) +y+=+120%2Fx+
By substitution:
(2) +x%2A%28120%2Fx%29+%2B+4%2A%28120%2Fx%29+-+5x+=+140+
(2) +120+%2B+4%2A%28120%2Fx%29+-+5x+=+140+
(2) +4%2A%28120%2Fx%29+-+5x+=+20+
(2) +480%2Fx+-+5x+=+20+
(2) +480+-+5x%5E2+=+20x+
(2) +5x%5E2+%2B+20x+=+480+
(2) +x%5E2+%2B+4x+=+96+
Complete the square
(2) +x%5E2+%2B+4x+%2B+%284%2F2%29%5E2+=+96+%2B+%284%2F2%29%5E2+
(2) +x%5E2+%2B+4x+%2B+4+=+96+%2B+4+
(2) +%28+x+%2B+2+%29%5E2+=+100+
(2) +%28x+%2B+2+%29%5E2+=+10%5E2+
(2) +x+%2B+2+=+10+
(2) +x+=+8+
and, since
(1) +120+=+x%2Ay+
(1) +y+=+120%2F8+
(1) +y+=+15+
----------------
And, also,
(2) +120+=+%28+x%2B4+%29%2A%28+y+-5+%29+
+x+%2B+4+=+12+
+y+-+5+=+10+
-----------------
Rectangle r1 has dimensions 8 and 15
Rectangle r2 has dimensions 12 and 20
----------
check:
+A1+=+8%2A15+
+A1+=+120+
and
+A2+=+12%2A10+
+A2+=+120+
OK