Question

In square MNOP, with sides labeled M(4t+20) and N(7f+6), what are the values of t and f?

a) t = 5, f = 2
b) t = 4, f = 1
c) t = 6, f = 3
d) t = 3, f = 4

Answer 1

By setting the expressions for the sides of square MNOP equal to each other, we determined that t and f must satisfy the equation 4t+20 = 7f+6. The correct values are t = 5 and f = 2, which corresponds to option (a).

Step-by-step explanation:

To find the values of t and f in square MNOP with sides labeled M(4t+20) and N(7f+6), we must remember that all sides of a square are equal. Therefore, the expressions for the sides must be equal, leading to the equation 4t+20 = 7f+6. To solve for t and f, we can rearrange this equation:

• Subtract 20 from both sides: 4t = 7f - 14
• Divide both sides by 4: t = (7f - 14)/4

Now we compare the given options to see which one satisfies the equation. After trying each option:

• Option (a): t = 5, f = 2; plugging these values into our equation gives 5 = (7*2 - 14)/4 which is true, so option (a) is correct.