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` ...(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
RELATED QUESTIONS
Convert the following ratio to a percentage.
2 : 3
If 4x + 4 : 9x – 10 is the triplicate ratio of 4 : 5, find x.
Express the following ratios in its simplest form :
200:250
Two numbers are in the ratio of 3: 5. If 8 is added to each number, the ratio becomes 2 : 3. Find the numbers.
Ratio of the distance of the school from A’s home to the distance of the school from B’s home is 2 : 1.
(i) Who lives nearer to the school?
(ii) Complete the following table:
If x, y, and z are in continued proportion, then which of the following is true:
y : x = y : z
If a : b = 3 : 5, find (3a + 5b): (7a – 2b).
If `a/b = c/d = e/f`, prove that each ratio is `[(2a^3 + 5c^3 + 7e^3)/(2b^3 + 5d^3 + 7f^3)]^(1/3)`
In a college, out of 4320 students, 2300 are girls. Find the ratio of number of girls to the total number of students.
Given below is a Mathematical term.
Find the ratio of consonants to vowels in the term.
