Question

28
d 80 and 100
e 17 and 33
8 The HCF of two numbers is 8. One of the numbers is between 20 and 30. The other number is
between 40 and 60. What are the two numbers?
mime number. What is the next prime after 31?

Answer 1

Answer:

Let the length of the rectangle be x units and the breadth be y units.

Area of the rectangle=length×breadth

=x×y=xy sq. units

From the given information, we have,

(x+2)×(y−2)=xy−28

and(x−1)×(y+2)=xy+33

(x+2)×(y−2)=xy−28

=>xy−2x+2y−4=xy−28

=>−2x+2y=−24

=>−x+y=−12

=>x=y+12....(i)

Also,(x−1)×(y+2)=xy+33

=>xy+2x−y−2=xy+33

=>2x−y=35....(ii)

Substituting equation (i) in equation (ii), we get,

2x−y=35

=>2(y+12)−y=35

=>2y+24−y=35

=>y=11

Substituting y=11 in equation (i), we get,

x=y+12

=>x=11+12

=>x=23

Therefore, length of rectangle =x=23 units

and breadth of rectangle =y=11 units

Area of rectangle =xy=23×11=253 square units