You are here:

Basic Math/Maths-Ratios and proportion


The ratio of three numbers is 3:4:5 .If the sum of their squares is 450,What are these numbers ?

Hello, Dhananjay.

The first thing to do in this problem is to assign variables for each of the three numbers. Since the three numbers are in a 3:4:5 ratio, it is appropriate to let 3x equal the 1st number, 4x equal the second number, and 5x equal the third number.

Next, we need to write an equation. Since the sum of the numbers' squares equals 450, we can write 9x^2 + 16x^2 + 25x^2 = 450.

Next, combine like terms on the left side of the equation, giving you 50x^2 = 450. After that, divide both sides by 50, leaving you with x^2 = 9.

Finally, take the square root of both sides, giving you x = 3.

3 is not the answer, of course, because the problem asks what the numbers in the ratio are. So we then need to substitute 3 in for x in 3x, 4x, and 5x in the original ratio, giving us numbers of 9, 12, and 15.

Answer: 9, 12, 15.

You will find that these numbers will fit into the ratio of 3:4:5, and that the sum of their squares will equal 450.

I hope this helps.


Basic Math

All Answers

Answers by Expert:

Ask Experts


John Zalewski


I can help you solve problems involving fractions, decimals, ratios, and algebra. I can teach you how to do math faster, and even in your head. I can teach math definitions, and help you study, if necessary. Please do not ask any graphing, trigonometry, or calculus questions. Try to work through homework questions before asking for assistance.


I routinely process numbers of all kinds in my head, without need of a calculator.

I was an A math student while in high school.

©2017 All rights reserved.