Advertisements
Advertisements
प्रश्न
If `"x"/("b + c - a") =" y" /("c + a - b") = "z"/("a + b - c")` , then prove that each ratio is equal to the ratio of `("x + y+z")/("a + b + c")`
Advertisements
उत्तर
`"x"/("b + c - a") =" y" /("c + a - b") = "z"/("a + b - c") = "k"`
x = k (b + c- a)
Y = k (c+a-b)
z = k (a+b-c)
Now ,
`("x + y+z")/("a + b + c")`
`= ("k"("b + c - a") + "k" ("c + a - b")+ "k" ("a + b - c"))/("a + b + c")`
`= ("k" ("b + c - a + c + a - b + a + b - c"))/("a + b + c")`
`= ("k"("a + b + c"))/("a + b + c") = "k"`
Hence ,
`"x"/("b + c - a") =" y" /("c + a - b") = "z"/("a + b - c") = ("x + y+z")/("a + b + c")`
Proved.
APPEARS IN
संबंधित प्रश्न
By increasing the cost of entry ticket to a fair in the ratio 10 : 13, the number of visitors to the fair has decreased in the ratio 6 : 5. In what ratio has the total collection increased or decreased?
If `(a + b)/(am + bn)= (b + c)/(mb + nc )= (c + a)/(mc + na)` prove that each of theseccc `2/(m+n)`provided a + b + c ≠ 0
Find the sub-duplicate ratio of the following :
x6 : y4
Two numbers are in the ratio 7 : 10. If 8 is added to each number, the ratio becomes 3 : 4. Find the nLimbers.
Find the third proportional of 1.6 and 0.8
The length of a pencil is 18 cm and its radius is 0.4 cm. Find the ratio of its length to its diameter.
Which of the following numbers are in continued proportion:
3, 6 and 15
Find the sub-triplicate ratio of 27a3 : 64b3
If A: B = `(1)/(4) : (1)/(5)` and B : C = `(1)/(7) : (1)/(6)`, find A : B : C.
In an election, the votes cast for two of the candidates were in the ratio 5 : 7. If the successful candidate received 20734 votes, how many votes did his opponent receive?
