Question

1. four times the sum of f and g is identical to six times g.
2. the area a of a square is the length of a side (ell) squared.
3. the perimeter p of a triangle is equal to the sum of the lengths of sides a, b, and c.

Explanation:

Step1: Translate 12

Translate the verbal - description into an equation. "Four times the sum of \(f\) and \(g\)" is \(4(f + g)\), and "six times \(g\)" is \(6g\). So the equation is \(4(f + g)=6g\).

Step2: Translate 13

The area formula for a square. The area \(A\) of a square with side - length \(\ell\) is given by \(A=\ell^{2}\).

Step3: Translate 14

The perimeter formula for a triangle. The perimeter \(P\) of a triangle with side - lengths \(a\), \(b\), and \(c\) is \(P=a + b + c\).

Answer:

1. \(4(f + g)=6g\)
2. \(A = \ell^{2}\)
3. \(P=a + b + c\)