A rectangular carpet has area 120m2 and perimeter 46 metres. The length of its diagonal is

(a) 15m (b) 16m (c) 17m (d) 20m

Suppose l and b be the length and breadth of the rectangular carpet respectively.
Then, area of rectangular carpet = lb = 120 m2
l = 120b.... (i)
And perimeter of rectangular plot = 2l+b = 46 m
2120b+b = 46            {using (i)}120b+b = 462120+b2b = 23120+b2 = 23b b2-23b+120 = 0 b2-15b-8b+120 = 0 bb-15-8b-15 = 0 b-8b-15 = 0 b-15 = 0 and b-8 = 0  b = 15 and b = 8
When b = 15, then l = 12015 = 8
And when b = 8, then l = 1208 = 15
This means dimensions of rectangular plot is 15 m by 8 m.

Therefore, diagonal of rectangular plot = 152+82 = 289 = 17 m
 

  • 0
What are you looking for?