Question

Edgar builds a sand castle with a rectangular base. The side lengths of the base are 25 in. And 16 in. He wants to surround the castle's base with a moat that is w inches wide. Write a quadratic function A in standard form to represent the combined area taken up by the castle and the moat.

Answer 1

Answer:

$A=4w^2+32w+400$

Step-by-step explanation:

-Given the castle dimensions is 25in by 16 in.

-And the moat's width is w:

The moat's width will increase the castle's dimension bytwice it's width, 2w:

#The castles area is thus calculated as:

$A=lw\\\\=(25+2w)(16+2w)\\\\=400+80w+32w+4w^2\\\\=4w^2+32w+400$

Hence, the combined area of the boat is given as $A=4w^2+32w+400$