priyalmishra1122
Answered

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The ratio of two positive numbers is 3:4. The sum
of their squares is 400. What is the sum ofthe num-
bers?​

Sagot :

kathrynlizzy

Answer:

12 and 16.

Step-by-step explanation:

Let both positive numbers be x and y.

3/4 = x/y....... equation 1

x² + y² = 400..... equation 2

From equation 1

3/4 = x/y

Cross multiply

3y = 4x

Divide both sides by 3

y = 4x/3

Substitute y = 4x/3 into equation 2

x² + y² = 400

x² + (4x/3)² = 400

x² + 16x²/9 = 400

Multiply through by 9

9x² + 16x² = 3600

25x² = 3600

Divide both sides by 25

x² = 3600/25

x² = 144

Take the square root of both sides

x = √144

x = 12

Substitute x = 12 into equation 1

3/4 = x/y

3/4 = 12/y

Cross multiply

3y = 12 x 4

3y = 48

Divide both sides by 3

y = 48/3

y = 16

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