The perimeter of a rectangle is 44cm and its area is 120cm sq find its length and breadth
Answers
Answer:
length = 12 cm
breadth=10 cm
Step-by-step explanation:
let, length = l and breadth = b
we know that,
perimeter of rectangle = 2(l+b)
area of rectangle = l×b
note: for the calculation part we have not written the units but we can add them later
thus,
area ⇒ 120cm²= l×b ---- Equation (i)
perimeter ⇒ 44cm =2(l+b)
⇒ 22 = (l+b) [lets try substituting l]
⇒ 22-b = l
∴l=22-b ---- Equation (ii)
substitute (ii) in (i),
∴120= (22-b)×b
⇒120=22b-b²
⇒b²-22b+120=0 [-10-12= -22 ; -10 × -12= 120]
⇒b²-10b-12b+120=0 [By factorization]
⇒b(b-10)-12(b-10)=0
⇒(b-12)(b-10)=0
∴b can be 12 or 10
Now in Eq(i) substitute for both values of b,
l=120÷10 or l= 120÷12
∴l=12 or 10
∵length is always longer than the breadth, we take
length= 12 cm and breadth = 10cm