Question

Question 3

The perimeter of a rectangle is 42 cm and its area is 20 cm²

a) What is the sum of length and breadth?

b) Find the length and breadth ?

Answer 1

Answer:

l + b = 21 cm, (20,1) cm and (1,20) cm    

Step-by-step explanation:

Now,

Given

Perimeter = 42 cm (i)

Area = 20 cm² (ii)

so from (i)

2(l + b) = 42

l + b = 42 / 2

l + b = 21 cm---(iii) answer to (a) part

From (ii),

lb = 20 cm²

l = 20 / b

Substituting the value of l in (iii),

20/b + b = 21

we get (after LCM),

(20 + b²) / b = 21

20 + b² = 21b

b² - 21b + 20 = 0 (iv)

So, we arrive at a quadratic equation

Now,

Product should be = 20b²

and Sum should be = -21b

so the numbers are = -20b and -1b

Plugging the split middle term in (iv),

b² - 20b - b + 20 = 0

b(b - 20) - 1(b - 20) = 0

(b - 1) (b - 20) = 0

so either (b - 1) = 0

or (b - 20) = 0

so b =( 1 or 20 ) cm

Plugging value of b in (iii),

when b = 1,

l + 1 = 21

so l = 20 cm

when b = 20,

l + 20 = 21

so l = 1 cm

so possible values of length and breadth respectively are,

(20,1) cm and (1,20) cm