Advertisements
Advertisements
प्रश्न
If x, y, z are in continued proportion, prove that: `(x + y)^2/(y + z)^2 = x/z`.
Advertisements
उत्तर
x, y, z are in continued proportion
Let `x/y = y/z = k`
Then y = kz
x = yk
= kz × k
= k2z
Now L.H.S.
= `(x + y)^2/(y + z)^2`
= `(k^2 z + kz)^2/(kz + z)^2`
= `{kz(k + 1)}^2/{z(k + 1)}^2`
= `(k^2z^2(k + 1)^2)/(z^2(k + 1)^2)`
= k2
R.H.S. = `x/z`
= `(k^2z)/z`
= k2
∴ L.H.S. = R.H.S.
APPEARS IN
संबंधित प्रश्न
If a, b and c are in continued proportion, prove that `(a^2 + b^2 + c^2)/(a + b + c)^2 = (a - b + c)/(a + b + c)`
Find the value of x in the following proportions : 3 : x = 24 : 2
Write (T) for true and (F) for false in case of the following:
36 : 45 : : 80 : 100
A transport company charges Rs 540 to carry 25 tonnes of weight. What will it charge to carry 35 tonnes?
In an army camp, there were provisions for 550 men for 28 days. But, 700 men attended the camp. How long did the provisions last?
Write the mean and extreme terms in the following ratios and check whether they are in proportion.
400 gm is to 50 gm and 25 rupees is to 625 rupees
A gets double of what B gets and B gets double of what C gets. Find A : B and B : C and verify whether the result is in proportion or not
Find the missing number in the box in the proportion:
`8/square = 3.2/4`
Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion.
200 mL : 2.5 litre and ₹ 4 : ₹ 50
The table, given below, shows the values of x and y, where x is proportional (directly proportional) to y.
| x | A | 24 | 15 |
| y | 12 | B | 20 |
The values of A and B are:
