Answer
True.
Work Step by Step
The area of the square is $=(side)^2$.
The given area of the square is $=9x^2$.
Equate both values.
$\Rightarrow (side)^2=9x^2$
Take square root both sides.
$\Rightarrow side=3x$
Given conditions are :-
One side is $7$ feet longer $=3x+7$.
and other side is $2$ feet shorter $=3x-2$
Area of the garden is equal to one side multiplied by other side.
Area $=(3x+7)(3x-2)$
Apply distributive property.
Area $=3x\cdot 3x+3x\cdot (-2)+7\cdot (3x)+7\cdot(-2)$
Simplify.
Area $=9x^2-6x+21x-14$
Add like terms.
Area $=9x^2+15x-14$
The given statement is true.
