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`
⇒ a = bk and 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(b^2k^2 + b^2)/(sqrt(d^2k^2 + d^2)`
= `(b(sqrt(k^2 + 1)))/(d(sqrt(k^2 + 1))) = b/d`
L.H.S. = R.H.S.
Hence proved.
APPEARS IN
संबंधित प्रश्न
If x, y, z are in continued proportion, prove that `(x + y)^2/(y + z)^2 = x/z`
If `(4m + 3n)/(4m - 3n) = 7/4`, use properties of proportion to find m : n
Find the value of the unknown in the following proportion :
c
Find the mean proportion of: `(1)/(12) and (1)/(75)`
Verify the following:
39 : 65 : : 141 : 235
40 men can finish a piece of work in 26 days. How many men will be needed to finish it in 16 days?
If a, b, c, d are in proportion, then
If `a/c = c/d = c/f` prove that : (b2 + d2 + f2) (a2 + c2 + e2) = (ab + cd + ef)2
If a, b, c and d are in proportion, prove that: (5a + 7b) (2c – 3d) = (5c + 7d) (2a – 3b).
If a, b, c and d are in proportion, prove that: `(a^2 + b^2)/(c^2 + d^2) = "ab + ad - bc"/"bc + cd - ad"`
