Question

Gessenia is having trouble interpreting how the constants within each expression can be represented in the given scenario. Draw a model or write an expression that explains this term.

Answer 1

Answer:

The height and  width of the interior tile =  3·x + 4 - 4 = 3·x and 2·x + 4  - 4= 2·x

Please see attached diagram

Step-by-step explanation:

The given parameters are;

The given rectangular floor tile  with width = 3·x + 4 and height = 2·x + 4

Where, x is in centimetres

The interior tile maintains a height to width ration of 2:3

The dimension of the trim border = 2 cm

Therefore;

The relationship between the width and height of the interior and exterior tiles is given as follows

Width of exterior tile = Width of interior tile + 2 × The dimension of the trim border

Which gives;

Width of exterior tile = Width of interior tile + 2 × 2 = Width of interior tile + 4

Height of exterior tile = Height of interior tile + 2 × The dimension of the trim border

Height of exterior tile = Height of interior tile + 2 × 2 = Height of interior tile + 4

Where the interior tile maintains a height to width ration of 2:3, we have;

For a unit length x, The height and the width of the interior tiles are 2·x:3·x

Therefore, for a given height 2·x, the width will be 3·x

Given the width of the exterior tile =  3·x + 4

The height of the exterior tile will then be 2·x + 4 and the width of the exterior tile will be 3·x + 4

The sides ratio of the interior tiles remain 2·x:3·x = 2/3