the ratio 4 : 56 is same as
Answers
Answer:
AP formed on dividing 56 into 4 parts will be
8 , 12 , 16 , 20
Step-by-step explanation:
Let, 56 is divided in 4 parts i.e,
a - 3 d , a - d , a + d , a + 3 d
which are in AP
so,
→ a - 3 d + a - d + a + d + a + 3 d = 56
→ 4 a = 56
→ a = 56 / 4
→ a = 14
Now,
as given that ratio of product of extremes and means is 5 : 6
therefore,
→ [(a - 3 d)(a + 3 d)] / (a - d)(a + d) = 5 / 6
→ (a² - 9 d²) / (a² - d²) = 5 / 6
( cross multiplying )
→ 6 a² - 54 d² = 5 a² - 5 d²
→ a² - 49 d² = 0
( putting a = 14 )
→ (14)² - 49 d² = 0
→ 196 = 49 d²
→ d² = 196 / 49
→ d = ± 2
Therefore,
on putting d = 2
four parts will be
→ a - 3 d = 14 - 3 ( 2 ) = 8
→ a - d = 14 - 2 = 12
→ a + d = 14 + 2 = 16
→ a + 3 d = 14 + 3 (2) = 20
(on taking d = -2 we will get the same A.P.)
Answer:
1:14
Step-by-step explanation:
Here we will simplify the ratio 4:56 for you and show you how we did it.
To simplify the ratio 4:56, we find the greatest common divisor of 4 and 56, and then we divide 4 and 56 by the greatest common divisor.
The greatest common divisor that you can use to simplify 4:56 is 4. Which means the answer to ratio 4:56 simplified is:
1:14