Triangle ABC has vertices at A (3,5), B (5, 7) and C (7,5).
Lisa believes that the perimeter of A ABC is 12 square units.
Why is Lisa incorrect?

Perimeter of Triangle ABC= 9.6

Step-by-step explanation:

I used a graph, and ploted the points of A, B, and C. You can then see that the base of the triangle is "4." To find the length of line segments AB and BC you can "cut" the triangle in half down point B and use that as it's height. You take the height (2) and the new base (also 2) and use the Pythagorean Theorem to find both AB and BC. Pythagorean Theorem is a^2+b^2=c^2.

You fill in "a" and "b" with the height and the base. So your equation would be 2^2+2^2=c^2. That would become 4+4=c^2, and that would become 8=c^2. Then you square root "8" to find "c." c = 2.8, meaning line segments AB and BC = 2.8.

You finally take AB+BC+CA to find your correct perimeter. (2.8+2.8+4= 9.6)

(Sorry it was long, but hope I helped!)

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752