Question

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.

Answer 1

See Explanation

Explanation:

Given

`Total = x^2 + 14x + 24`

`Area\ I = x^2`

`Area\ IV = 24`

Required

True about area II and III

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

If the total area is:

`Total = x^2 + 14x + 24`

And there are 4 areas, then;

`Total = Area\ I + Area\ II + Area\ III + Area\ IV`

Rewrite as:

`Total = Area\ I + Area\ IV+ Area\ II + Area\ III`

This gives:

`x^2 + 14x + 24 = x^2 + 24+ Area\ II + Area\ III`

Collect like terms

`x^2 -x^2 + 14x + 24 -24= Area\ II + Area\ III`

`14x = Area\ II + Area\ III`

Rewrite as:

`Area\ II + Area\ III = 14x`

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