5. (a) A surveyor found that a rectangular playground is 20 m long and 13 m wide, corrected to the nearest metre. Suppose the actual length of the playground is x m and the breadth is y m. Write down an inequality for the range of the values of (i)x (ii) y
Let breadth of the rectangular playground =b Length of the rectangular playground =(b+2) Area of rectangular playground = Length × Breadth ⇒195=(b+2)×b ⇒195=b 2 +2b ⇒b 2 +2b−195=0 ⇒b 2 +15b−13b−195=0 ⇒b(b+15)−13(b+15)=0 ⇒(b−13)(b+15)=0 ⇒b=13 or b=−15 Value b of can't be negative. So b=13 Therefore, breadth of the rectangular playground =13 m and length of the rectangular playground =15 m
