Advertisements
Advertisements
प्रश्न
If `a/b = c/d`, show that: `(a + b) : (c + d) = sqrt(a^2 + b^2) : sqrt(c^2 + d^2)`
Advertisements
उत्तर
Let `a/b = c/d = k` ...(Say)
`=>` a = bk, c = dk
L.H.S = `(a + b)/(c + d)`
= `(bk + b)/(dk + d)`
= `(b(k + 1))/(d(k + 1))`
= `b/d`
R.H.S = `sqrt(a^2 + b^2)/sqrt(c^2 + d^2)`
= `sqrt((bk)^2 + b^2)/sqrt((dk)^2 + d^2)`
= `sqrt(b^2(k^2 + 1))/sqrt(d^2(k^2 + 1))`
= `sqrt(b^2)/sqrt(d^2)`
= `b/d`
∴ L.H.S = R.H.S
APPEARS IN
संबंधित प्रश्न
If A : B = 2 : 5 and A : C = 3 : 4, find: A : B : C.
Find triplicate ratio of 1 : 3
Find the compounded ratio of the following:
15: 16 and 8 : 5
Find the value of x, when 2.5 : 4 = x : 7.5.
In the example below, find the ratio of the first number to the second.
84, 60
The income of a man is increased in the ratio of 10 : 11. If the increase in his income is Rs 600 per month, find his new income.
Write the following ratio in the simplest form:
48 min : 2 hours 40 min
The boys and the girls in a school are in the ratio 9 : 5. If the total strength of the school is 448, find the number of girls.
The ratio of 10 kg to 100 kg is 1 : 10
In the following figure, division represents 1 cm:
Express numerically the ratios of the following distances:
CE : DI
