Question

the perimeter of the rectangle is 40cms and it's area is 96sqcms calculate its length and breadth
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Answer 1

Answer:

Step-by-step explanation:

Length=L

Breadth=B

L*B=96SQcms(equ - 1).

2(L+B)=40SQcms.

L+B=20sqcms(equ - 2).

L=20-B.

Substitute in(equ - 1).

L*B=96.

20-B*B=96.

B^2 - 20B - 96=0

B^2 +4B - 24B - 96 =0

B(B+4)-24(B+4)=0

(B-24)(B+4)=0

B=24 (OR) - 4

BREADTH IS A POSITIVE VALUE

SO, B=24

Substitute in (equ - 2)

L + B = 20

L + 24=20

L= - 4

(OR)

L*B=96

L+B=20.

FACTORS OF 96 ARE =

2*48

3*32

4*24

6*13

8*12

IF L=12

B=8

L*B=96

12*8=96

96=96

L+B=20

12+8=20

20=20

SO,L=12cm.

B=8 cm.

Answer 2

PERIMETER OF RECTANGLE=40cm

AREA=96cm^2

$\huge \mathfrak{perimeter \: of \: rect. = 2(l + b}$

40=2(l+b)

l+b=20----------------------i

$\huge \mathfrak{area \: of \: rect = l \times b}$

lxb=96-------------------ii

from(i)

l=20-b

put in (ii)

(20-b)b=96

20b-b^2=96

b^2-20b+96=0

b^2-12b-8b+96=0

b(b-12)-8(b-12)=0

(b-12)(b-8)=0

b-12=0 &b-8=0

$\huge \mathbb{b = 12 \: or \: b = 8}$

put in equation (i)

when b=12,l=8

when b=8,l=12

•°•

$\huge \mathfrak{l = 12cm \: andb = 8cm}$

HOPE IT HELPS YOU☺☺✊✊