veespot15
Answered

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The height of Moyo and that of
Adamu differs by 9. The difference of the squares of their height is 120.
Find their heights.​

Sagot :

elcharly64

Answer:

The height of Moyo is

[tex]\frac{67}{6}[/tex]

The height of Adamu is

[tex]\frac{13}{6}[/tex]

Step-by-step explanation:

Equations

To solve the problem, we assign the variable:

x = height of Moyo

Since Moyo is 9 units taller than Adamu:

x - 9 = height of Adamu

The difference of the squares of their heights is 120, thus:

[tex]x^2-(x - 9)^2=120[/tex]

Operating:

[tex]x^2-(x^2-18x+81)=120[/tex]

[tex]x^2-x^2+18x-81=120[/tex]

Simplifying:

[tex]18x-81=120[/tex]

Adding 81:

[tex]18x=120+81=201[/tex]

Dividing by 18:

[tex]x=\frac{201}{18}=\frac{67}{6}[/tex]

The height of Moyo is

[tex]\frac{67}{6}[/tex]

The height of Adamu is

[tex]\frac{67}{6}-9=\frac{13}{6}[/tex]

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