Ananya D.

Let the length of the shorter side be x metres. 

The length of the diagonal= 60+x metres

The length of the longer side =30+x metres

Applying Pythagoras theorem, 

Diagonal²=longer side²+shorter side²

(60+x) ²= (30+x) ² + x²

3600+120x+x²=900+60x+x²+x²

2700+60x-x²=0

2700+90x-30x-x²=0

90(30+x)-x(30+x) =0

X=90, 

Shorter side is 90m,  longer side is 90+30=120m

1. X² -5x+2x-10=0

x(x-5) +2(x-5) =0

(X+2) (x-5) =0

X=-2, 5

2. √2x²+5x+2x+5√2=0

X(√2x+5) +√2(√2x+5) =0

(X+√2) (√2x+5) =0

X=-√2, -5/√2

3.  2x²+4x-3x-6=0

2x(x+2) -3(x+2) =0

(2x-3) (x+2) =0

X=3/2,  -2

5. (10x)²-2.(10x)(1)+1²=0

(10x-1)² =0

X=±1/10

well first ask yourself why do you want to study?  Is it for only getting better marks or you actually want to know the subject well. Here are a few steps you can try

? If you are starting a new topic/chapter, read the outline or theme of the chapter given in the beginning.

? Then start with a small section say a paragraph, read it and try to understand the key points and highlight them.

? Explain that topic in plain layman language to a friend/parents/your maid or even your pet(if they have that much patience). When you explain you get a lot of confidence

? Now go to the next topic and try to make a link.

? you can also make doodles/diagrams of your own when you explain , if you want.

?Try to google about that topic and write small points in your book, that way you will have an edge over your classmates on this topic

? study in chunks..Don't just sir for 2-3 hours straight and study if you don't want to. Study for 30 minutes and take a 5 min break..come back refreshed again.

? If you are a board student then practise a lot of question papers too

? And if you have maths and physics numericals do practise them a lot, that's the only way you can ace.

Happy studying,

Cheers