Advertisements
Advertisements
Question
If a : b : : c : d, then prove that
2a+7b : 2a-7b = 2c+7d : 2c-7d
Advertisements
Solution
2a+7b : 2a-7b = 2c+7d : 2c -7d
`"a"/"b" = "c"/"d"`
Multiplying both sides by `2/7`
`=> "a"/"b" xx 2/7 = "c"/"d" xx 2/7`
`=> (2"a")/(7"b") = (2"c")/(7"d")`
Applying componendo and dividendo,
`(2"a" + 7"b")/(2"a" - 7"b") = (2"c" + 7"d")/(2"c" - 7"d")`
Hence, 2a+7b : 2a-7b = 2c+7d : 2c-7d
APPEARS IN
RELATED QUESTIONS
Using properties of proportion, solve for x. Given that x is positive:
`(2x + sqrt(4x^2 -1))/(2x - sqrt(4x^2 - 1)) = 4`
If x, y, z are in continued proportion, prove that `(x + y)^2/(y + z)^2 = x/z`
Find the third proportional to a2 – b2 and a + b.
If y is the mean proportional between x and z, show that :
xyz (x+y+z)3 =(xy+yz+xz)3
If `a = (b + c)/(2), c = (a + b)/(2)` and b is mean proportional between a and c, prove that `(1)/a + (1)/c = (1)/b`.
Determine if the following numbers are in proportion:
32, 48, 70, 210
In proportion, the 1st, 2nd, and 4th terms are 51, 68, and 108 respectively. Find the 3rd term.
If 24 workers can build a wall in 15 days, how many days will 8 workers take to build a similar wall?
If 2, 6, p, 54 and q are in continued proportion, find the values of p and q.
Find the missing number in the box in the proportions:
`3/8 = square/20`
