Two numbers are is the ratio 3:4. If the sum of their squares is 900 f

1.	Two numbers are is the ratio 3:4. If the sum of their squares is 900 find the two numbers.
Answer» Given \(\frac{x}{y} = \frac{3}{4},\)\(\frac{y}{z} = \frac{7}{9}\) Given sum of their squares = 900 (3x)² + (4x)²= 900 9x² + 16x² = 900 25x²= 900 ⇒ x² = \(\frac{900}{25}\) = 36 ⇒ x = 6 ∴ The numbers are 3(6) and 4(6) = 18 and 24

Two numbers are is the ratio 3:4. If the sum of their squares is 900 find the two numbers.

Answer»

Given \(\frac{x}{y} = \frac{3}{4},\)\(\frac{y}{z} = \frac{7}{9}\)

Given sum of their squares = 900

(3x)² + (4x)²= 900

9x² + 16x² = 900

25x²= 900

⇒ x² = \(\frac{900}{25}\) = 36 ⇒ x = 6

∴ The numbers are 3(6) and 4(6) = 18 and 24