find the length and breadth of a rectangular plot whose area is 660square metre and perimeter is 104metre

Step-by-step explanation:

let length=l

breadth=b

l×b=660

2(l+b)=104

l+b=104/2=52

b=52-l

l×(52-l)=660

52l-l²=660

l²-52l+660=0

l²-22l-30l+660=0

l(l-22)-30(l-22)=0

(l-22)(l-30)=0

l=22,30

when l=22,b=52-22=30

when l=30,b=52-30=22

l>b

so l=30m

b=22m

W = 22 m

L = 30 m

Step-by-step explanation:

given:

area is 660square metre and perimeter is 104metre

find:

the length and breadth of a rectangular plot

1. area of rectangle (A) = L x W

2. Perimeter of a rectangle (P) = 2L + 2W

where:

A = 660 m²

P = 104 m

solve for L using formula 1.

A = L x W

660 = L x W

L =  660 / W

solve W using formula 2 and use L = 660 / W

P = 2L + 2W

104 = 2 (660)  +  2W

               W

104W = 1320 + 2 W²

-2W² + 104W = 1320

solve W using quadratic equation:

W = 22 m; ( 30 m = L)

plugin W=22 into L =  660 / W to solve L:

L = 660 / 22

L = 30 m