Find three number in the ratio of $2:3:4$, the sum of whose square is $725$.
Given: Three number are in the ratio of $2:3:4$, the sum of whose square is $725$.
To do: To find the numbers.
Solution:
Ratio of the numbers$=2:3:4$
Let $2x,\ 3x$ and $4x$ be the three numbers in the given given ratio.
As given, sum of the squares of the numbers is $725$.
$\Rightarrow ( 2x)^2+( 3x)^2+( 4x)^2=725$
$\Rightarrow 4x^2+9x^2+16x^2=725$
$\Rightarrow 29x^2=725$
$\Rightarrow x^2=\frac{725}{29}$
$\Rightarrow x^2=25$
$\Rightarrow x=\sqrt{25}$
$\Rightarrow x=5$
Now, put the value of $x$ in $2x,\ 3x$ and $4x$,
$2x=2\times5=10$
$3x=3\times5=15$
$4x=4\times5=20$
Therefore, the numbers are $10,\ 15,\ 20$.
Related Articles
- Three number are in the ratio $2:3:4$. The sum of their cube is $0.334125$, find the numbers.
- Three numbers are In the ratio $2: 3: 4$. The sum of their cubes is $33957$. Find the numbers.
- Three number are in the ratio 1:2:3 . The sum of their cubes is 79092 . Find the numbers
- Three numbers are in the ratio 2: 3: 5 . The sum of their cubes is 34560 . Find the numbers.
- Three numbers are in the ratio 1:2:3. The sum of their cubes is 98784. Find the numbers.
- The number of pairs of two digit square numbers, the sum or difference of which are also square numbers is(1) 0(2) 1(3) 2(4) 3
- Three numbers \( A, B, C \) are in the ratio \( \frac{1}{2}: \frac{2}{3}: \frac{3}{4} \) and their sum is 276. Find the numbers.
- The sum of three numbers in A.P. is $30$ and the ratio of the first number to the third the number is $3:7$. Find the numbers.
- Three cubes of a metal whose edges are in the ratio \( 3: 4: 5 \) are melted and converted into a single cube whose diagonal is \( 12 \sqrt{3} \mathrm{~cm} \). Find the edges of the three cubes.
- Find the area of the quadrilaterals, the coordinates of whose vertices are$(-4, -2), (-3, -5), (3, -2), (2, 3)$
- Find the smallest and greatest angle of a pentagon whose angle are in the ratio $6:3:2:5:4$.
- Three numbers are to one another 2:3:4. The sum of their cubes is 0.334125. Find the numbers.
- Find the lengths of the sides of a triangle whose perimeter is 12 cm and the lengths of the sides are in the ratio $3:2:4$.
- The sum of a number and its square is $\frac{63}{4}$, find the numbers.
- Find the angles of a triangle which are in the ratio 2: 3: 4.
Kickstart Your Career
Get certified by completing the course
Get Started
To Continue Learning Please Login
Login with Google