Question

A square quilt for a child’s bed has a border made up of 44 pieces with an area of x each, and 4 small squares with an area of 1 square inch each. The main part of the quilt is made of 121 squares with an area of x 2 each. Find an expression for the area of the quilt.

Answer 1

Answer:

A = ( 11x + 2 )²

Step-by-step explanation:

To find the total area of the quilt, we need to add up all the areas given:

If the border has 44 pieces with an area of x each one, that area is 44x.

The area of 4 squares of 1 in² each is 4×1 in² = 4 in².

The main part is made up of 121 squares with an area of x², which is 121x².

Adding those areas up, we get the expression for the total area:

A = 121x² + 44x + 4

You can easily notice that 121 = 11² and 4 = 2². If you double its product (2·11·2) = 44

So:

A = ( 11x + 2 )²