A square picture frame occupies an area of 112 ft2. What is the length of each side of the picture in simplified radical form?
A = a^2
112 = a^2
sqrt 112 = a
sqrt 16 * sqrt 7 = a
4 sqrt 7 = a
so 4 sqrt 7 is the length of each side
Answer:
\(4\sqrt{7}\ ft\)
Step-by-step explanation:
we know that
The area of a square is equal to
\(A=b^{2}\)
where
b is the length side of the square
In this problem we have
\(A=112\ ft^{2}\)
substitute in the formula and solve for b
\(112=b^{2}\)
Square root both sides
\(b=\sqrt{112} \ ft\)
Simplify
\(b=\sqrt{2^{4}*7} =4\sqrt{7}\ ft\)