Suppose the total area is represented by the equation x^2+14x+24. If the area 1 is x^2 square units and area IV is 24 units, what must be true about area II and area III.

Question

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Respuesta :

MrRoyal MrRoyal · Answer 1 · 2021-04-11T16:28:27+02:00

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]Total = x^2 + 14x + 24[/tex]

[tex]Area\ I = x^2[/tex]

[tex]Area\ IV = 24[/tex]

Required

True about area II and III

The question is incomplete; so, I will answer using general knowledge.

If the total area is:

[tex]Total = x^2 + 14x + 24[/tex]

And there are 4 areas, then;

[tex]Total = Area\ I + Area\ II + Area\ III + Area\ IV[/tex]

Rewrite as:

[tex]Total = Area\ I + Area\ IV+ Area\ II + Area\ III[/tex]

This gives:

[tex]x^2 + 14x + 24 = x^2 + 24+ Area\ II + Area\ III[/tex]

Collect like terms

[tex]x^2 -x^2 + 14x + 24 -24= Area\ II + Area\ III[/tex]

[tex]14x = Area\ II + Area\ III[/tex]

Rewrite as:

[tex]Area\ II + Area\ III = 14x[/tex]

So, the sum of areas III and IV must be 14x