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
Find the number which bears the same ratio to `7/33` that `8/21` does to `4/9`.
What quantity must be subtracted from each term of the ratio 9 : 17 to make it equal to 1 : 3?
Rs. 720 is divided between x and y in the ratio 4:5. How many rupees will each get?
If x : y = 2 : 3, and y : z = 4 : 7, find x : y : z
Fill in the place holder:
A car travels 288 km in 4 hours and a train travels 540 km in 6 hours. The ratio of their speeds is
25 kg : 20 g = 50 kg : 40 g
In a school, the ratio of the number of large classrooms to small classrooms is 3 : 4. If the number of small rooms is 20, then find the number of large rooms.
A doctor reports blood pressure in millimeters of mercury (mm Hg) as a ratio of systolic blood pressure to diastolic blood pressure (such as 140 over 80). Systolic pressure is measured when the heart beats, and diastolic pressure is measured when it rests. Refer to the table of blood pressure ranges for adults.
| Blood Pressure Ranges | |||
| Normal | Prehypertension | Hypertension (Very High) |
|
| Systolic | Under 120 mm Hg | 120-139 mm Hg | 140 mm Hg and above |
| Diastolic | Under 80 mm Hg | 80-89 mm Hg | 90 mm Hg and above |
Manohar is a healthy 37 years old man whose blood pressure is in the normal category.
- Calculate an approximate ratio of systolic to diastolic blood pressures in the normal range.
- If Manohar’s systolic blood pressure is 102 mm Hg, use the ratio from part (a) to predict his diastolic blood pressure.
- Calculate the ratio of average systolic to average diastolic blood pressure in the prehypertension category.
Given below is a Mathematical term.
Find the ratio of consonants to vowels in the term.
