Question

The ratio of length to breadth of a rectangular field is 4:3.if it's diagonal is 200meters ,the area of the field in square meters is

Answer 1

Step-by-step explanation:

Let the common multiplier of the given ratios be x.

Therefore,

Length = 4x

Breadth = 3x

Hence,

$(4x)^{2} + (3x)^{2} = (200)^{2} \\ 16 {x}^{2} + 9 {x}^{2} = 40000 \\ 25 {x}^{2} = 40000 \\ {x}^{2} = \frac{40000}{25} \\ {x}^{2} = 1600 \\ x = \sqrt{1600} \\ x = 40 \\ \implies \: 4x = 4 \times 40 = 160 \: m \\ \implies \: 3x = 3 \times 40 = 120 \: m \\ Area \: of \: field = 160 \times 120 \\ = 19200 \: {m}^{2}$