the area of a square can be quadrupled by increasing the side length and width by 4 inches. what is the side length?

Mathematics

2 answers:

Olenka [21]3 years ago

5 0

Let the original side of the square be x inches.When sides are increased by 4 inches the sides are x+4 inches.

Area of square with side x inches= $x^{2}.$

Area of square with sides x+ inches= $(x+4)^{2}.$

According to question:The area of a square can be quadrupled by increasing the side length and width by 4 inches.\

Or $4x^{2}=(x+4)^{2}$

Expanding we have:

$4x^{2}=x^{2}+8x+16.$

Or, $3x^{2}-8x-16=0.$

Factoring,

(3x+4)(x-4)=0

3x+4=0 or x=4

x= $-\frac{4}{3}.$ Or x=4.

Sides can not be negative so x=4.

The sides of the square will be 4 inches.

Semmy [17]3 years ago

3 0

The number could be anything because whatever it is it can be quadrupled

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