Question

Find the number.
2. The diagonals of a rectangular field is 60m more than the shorter side. If the longer side is 30m
more than the shorter side, Find the sides of the field.
3. Find the sum of all three digits number divisible by 7 leave a remainder ?​

Answer 1

☆Solution 2.

Let the length of shorter side be x metres.

The length of diagonal = 60+ x metres.

The length of the longer sides = 30 + x metres

Applying Phythagoraus 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

☆Solution3

The formula to find the numbers of terms in an arithmetic sequence is given by

n = [(l - a) / d] + 1

Substitute a = 105, l = 994 and d = 7.

n  =  [(994 - 105) / 7] + 1

n  =  [889/7] + 1

n  =  127 + 1

n  =  128

So, number of 3 digit numbers divisible by 7 is 128.