SOLUTION: 2 consecutive sides of a rectangle are in the ratio 5 to 7. the area is 140 cm. find the dimensions of rectangle

Algebra ->  Surface-area -> SOLUTION: 2 consecutive sides of a rectangle are in the ratio 5 to 7. the area is 140 cm. find the dimensions of rectangle      Log On


   

Question 838167: 2 consecutive sides of a rectangle are in the ratio 5 to 7. the area is 140 cm. find the dimensions of rectangle
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the short side of the rectangle
Let +b+ = the long side of the rectangle
Set up the ratio:
(1) +5%2F7+=+a%2Fb+
You are given that:
(2) +a%2Ab+=+140+
-----------------------
Multiply both sides of (1) by +7b+
(1)) +5b+=+7a+
and
Divide both sides of (2) by +a+
(2) +b+=+140%2Fa+
Substitute (2) into (1)
(1) +5%2A%28140%2Fa%29+=+7a+
(1) +5%2A140+=+7a%5E2+
(1) +a%5E2+=+5%2A20+
(1) +a%5E2+=+100+
(1) +a+=+10+
and, since
(2) +b+=+140%2Fa+
(2) +b+=+140%2F10+
(2) +b+=+14+
The sides are 10 cm and 14 cm