Question

the ratio of the length and breadth of a rectangular page is 5:3.If the area of the page is 2940m*2 find the fencing cost at the rate of 8 per metre

Answer 1

let the no. of side be x 
so it would be 5x and 3x 
now as we know the area of rectangle is length x breadth
so given area is 2940 m*2 
now the equation would be ..... 
3x  multiplied by 5x = 2940
15x*2 = 2940 
x*2 = 2940/ 15 that gives us 196
now ....,,,,,,
x*2 is equal to 196
the square root of 196 is 14 ....

now we can find out the sides ......
3x = 3 x 14 = 42m
5x = 5 x 14 = 70 m 

the rate of fencing is ....... 8 per metre 
so first of all we will find out the perimeter of the rectangular sheet that is ...
2[l+b]
2 x [ 42+70]
2x 112
224 m 

now the rate of fencing is 224 x 8
that is Rs 1792 /-

Answer 2

Let x be the common factors of the ratio of length and breath of the rectangular page.
Note: x÷x = 1

Thus ratio = length : breadth
ratio = 5: 3
ratio = 5x : 3x

Thus, Length = 5x ; breadth = 3x

If the area of rectangle = length × breadth
So, Area of rectangle = 2940m² (given)
So, 5x × 3x = 2940m².
So, 15x² = 2940m².
So, x² = 2940m²
So, x = √[(2940 ÷ 15)m²]
So, x = √[196m²]
So, x = √(2×7×2×7m²)
So, x = √[ (2×2) × (7×7)×(1m × 1m)]
So, x = 2 × 7 × 1m
So, x = 14m

If length = 5x,
So, lengh= 5 × 14m = 70m.

If breadth = 3x.
So, breadth = 3×14m= 42m.

If the perimeter of rectangular page
= 2 (length + breadth)
=2 (70m + 42m)
=2× 112m
=224m

If cost bodering or fencing for 1m² = Rs 8.
So, cost of fencing or bodering for 224m
= 224 × Rs 8
= Rs 1792.