Question

Square A has a side length $ \left( {2x - 7} \right) $ and square B has side length $ \left( { - 4x + 18} \right) $ how much bigger is the perimeter of square B than square A?

Answer 1

Hint: To solve this problem we should know about basics term like :
Perimeter: the sum of total length of outer periphery of a given shape it is its perimeter.
The perimeter for the square having side length is $ a $ is $ 4a $ .

Complete step by step solution:
As given, $ \left( {2x - 7} \right) $ Side length of square B is $ \left( { - 4x + 18} \right) $
So, the perimeter of square A $ = 4 \times \left( {2x - 7} \right) = 8x - 28 $ .
So, the perimeter of square B $ = 4 \times \left( { - 4x + 18} \right) = - 16x + 72 $ .
To find how much bigger is the perimeter of square B than square A.
We have to subtract the perimeter of square B with perimeter of square A. we get,
  $ perimeter\,of\,square\,B - perimeter\,of\,square\,A $
By keeping value in it. We get,
  $ \Rightarrow - 16x + 72 - \left( {8x - 28} \right) = - 16x + 72 - 8x + 28 $
  $ \Rightarrow - 16x + 72 - 8x + 28 = - 24x + 100 $
Hence the perimeter of square B is $ - 24x + 100 $ is greater than the perimeter of square A.

Note: Algebraic equation used in determining the length of side of variable or unknown square or geometrical shape. To find the length of side of unknown shape we will let any value for its length then we will equate it with given equation. So, we will get its value. It is used in construction of dams, building to calculate the value suitable for constructions.