Question

area =100
perimeter =60
length =?
bread =?

Answer 1

Let the length be l units,


Given, perimeter = 60 units

2( length + breadth ) = 60 units

l units + breadth = 30 units

breadth = 30 units - l units



Therefore, breadth = 30 units - l units



Given , area = 100 unit²

length × breadth = 100 units²

l × ( 30 - l ) unit² = 100 unit²

30l - l² = 100

l² - 30l + 100 = 0





By Shri Dharacharya's formula ( quadratic formula ) ,


$l = \dfrac{30 \pm \sqrt{(30) {}^{2} - 4(100\times 1)| } }{2 \times 1} \\ \\ \\ \\ l = \dfrac{30 \pm \sqrt{900 - 400} }{2} \\ \\ \\ \\ l = \dfrac{30 \pm \sqrt{500}}{2} \\ \\ \\ l = \frac{30 \pm \: 10 \sqrt{5}}{2} \\ \\ \\ l = 15 + 5 \sqrt{5} \: \: \: \: \: \: or \: \: \: \: \: \:15 - 5 \sqrt{5}$



if we take l = 15 + 5√5

length = 15 + 5√5

breadth = 30 - 15 - 5√5 = 15 - 5√5



if we take l = 15 - 5√5

length = 15 - 5√5

breadth = 30 - 15 + 5√5 = 15 + 5√5