Question

perimeter and area of rectangle is 28 and 40 find the length and breadth

Answer 1

perimeter
2(l+b)=28
l+b=14........(i)
l=14-b
area
l*b=40
(14-b)(b)=40
14b-b²=40
-b²+14b-40
b²-14b+40=0

Answer 2

If Length = 10, then Breadth = 4

If Length = 4, then Breadth = 10

Step-by-step explanation:

Perimeter of the Rectangle =  28

Area of the Rectangle = 40

Let the length of the rectangle = L

breadth of the rectangle = B

⇒ 2(L +B)  = 28

And L x B = 40

So, by  L x B = 40, we get  B = 40/LPut in the formula for perimeter.

⇒2(L +B)  = 2( L + $\frac{40}{L}$)  = 28

or, $\frac{2 \times (L^{2}  + 40) }{L}  = 28\\or, L^{2}  + 40 = 14L$

Hence, the equation becomes $L^{2}  -  14L + 40  = 0$

Solving for L , we get

(L-4)(L-10) = 0

⇒ either L = 4, or L = 10

if L = 4, B = 40/L = 10

if L =10, B = 40/ 10 = 4

So, L = 10 or 4

and B = 4 or 10