Advertisements
Advertisements
Question
If `a/b = c/d` Show that a + b : c + d = `sqrt(a^2 + b^2) : sqrt(c^2 + d^2)`.
Advertisements
Solution
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
RELATED QUESTIONS
Check whether the following numbers are in continued proportion.
1, 2, 3
Given four quantities p, q, r and s are in proportion, show that
q2(p - r) : rs (q - s) =(p2- q2- pq): ( r2-s2-rs).
Find the mean proportion of: (a – b) and (a³ – a²b), a> b
Find the value of x in each of the following proportions:
55 : 11 : : x : 6
A transport company charges Rs 540 to carry 25 tonnes of weight. What will it charge to carry 35 tonnes?
Choose the correct statement:
The length and breadth of a rectangular field are in the ratio 5 : 4. If the width of the field is 36 m, what is its length?
If b is the mean proportional between a and c, prove that a, c, a² + b², and b² + c² are proportional.
Are the ratios 25g: 30g and 40 kg: 48 kg in proportion?
10 books is to 15 books as 3 books is to 15 books
