Question

The perimeter of a rectangle is 42 cm it's area is 20 sq .cm
a)what is the sum of the length and breadth
b)Find the length and breadth

Answer 1

perimeter of rectangle=42cm
area of the rectangle=20cm²

a) perimeter= 2( l + b)
=>42 = 2( l + b)
=>42/2 = l + b
=>21 = l + b ------>( i )

b) From equation ( i ), we have:
l + b = 21
=>b = 21 - l
l + b = 21
=>l = 21 - b

Answer 2

The solution to a) and b) is 21 and 20 and 1.

Given - Perimeter and area

Find - a) sum of the length and breadth

b) the length and breadth

Solution - As per the known fact, the formula of perimeter is -

Perimeter = 2×(length + breadth)

Also, the formula of area is -

Area = length×breadth

Let length be represented as l and breadth be represented as b.

Now, keep the values in formula of perimeter to find sum of length and breadth

42 = 2×(l + b)

l + b = $\frac{42}{2}$

l + b = 21

b = 21 - l

Now, keep the value of breadth and area in the formula of area

20 = l×(21 - l)

20 = 21l - l²

l² - 21l + 20 = 0

l² - 20l - 1l + 20 = 0

l (l - 20) -1 (l - 20) = 0

(l - 20) (l - 1) = 0

Hence, the values of l are 20 and 1.

So, if length is 20, then breadth will be -

20 = 20 × b

b = 1 cm

And, if length is 1, then breadth will be -

20 = 1 × b

b = 20 cm

Thus, sum of length and breadth is 21 and length and breadth can be 20 and 1 and vice versa.

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