Diego plans to build an extension to his rectangular model bridge. Let x represent the increase, in centimeters, of the model's
length. The expression 2 1 (x + 8) represents the area of the model bridge, where 2 1 is the width, in centimeters, and (x + 8) represents the extended length, in centimeters, of the model. Which expression is equivalent to 2 1 (x + 8)?
If the expression 2 1 (x + 8) represents the area of the model bridge, where 2 1 is the width, in centimeters, and (x + 8) represents the extended length, the expression that is equivalent to 21(x+8) can be gotten by expanding the function. The expansion of the function will give the area of the rectangular model bridge as shown;
21(x+8) = 21x+ 168
The expression equivalent to 21(x+8) is therefore (21x+68)cm²
Note that the the unit of the value and function given is in cm therefore the unit of their equivalent expression will be in cm²
According to the question, 21 ( x + 8) represents the area of the extended model bridge.
Since the model bridge is rectangular, the length is x + 8 cm while the width is 21 cm. Hence, the area of the rectangular model bridge will be 21 × (x + 8) using Length (L) × Breadth (B) formula.
21 × (x +8)
= 21 (x +8)
Opening the bracket, we will have:
21x + 168 cm.
21x + 168 is equivalent of 21 (x + 168) just that the former expression is an expanded form.
