Question

if the area of a rectangle is 24 cm square and its perimeter is 22 metre then its sides in meter are​

Answer 1

$\huge\boxed{\fcolorbox{black}{red}{Answer}}$

Given-

$l \times b = 24 \\ 2(l + b) = 22 \\ l + b = 11 \\ l = 11 - b$

now,

$(11 - b)b = 24 \\ 11b - {b}^{2} = 24 \\ {b}^{2} - 11b + 24 = 0 \\ {b}^{2} - 8b - 3b + 24 = 0 \\ b(b - 8) - 3(b - 8) = 0 \\ b = 3 \\ b = 8$

substitute value of b as 3,

$l = 11 - 3 \\ l = 8$

3cm and 11cm

0.3 m and 1.1 m

$<marquee>Thanks✨</marquee>$

Answer 2

hello mate!!!

Solution:

let the length be x m and breadth be y meter.

now,

we know,

area of a rectangle = l×b

24= x×y

24/y=x....(1)

also,

perimeter= 2(l+b)

22=2(x+y)

22/2=24/y+y

11=24/y+y.....(2)

multiplying (2) by y,

11y=24+y^2

now,

y^2-11y+24=0..... (required quadratic polynomial)

y^2-8x-3x+24=0...... (factorization)

y(y-8) -3(x-8) =0

(y-8) (y-3) =0

therefore,

y=8 or y=3

now,

we know,

length > breadth

8>3

hence, breadth must be 3 m

if y= 3

then,

24/y=x

24/3=8 m

therefore,

the length can be 8m

hence,

length= 8m and breadth= 3m

hope this helps!!! ❤☺✌