# Geometry / Algebra 1

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(a) The surface area of the prism shown is 314 square meters. Write an equation that u can solve to find the value of w.
side a=wm b=8m and c=(w+4)m (on the picture)
I'm guessing u use the formula surface area=2ab+2bc+2ac??? Well if so I need all that solved into y=ax*2+bx+c so I can solve step (b) and (c) for (b) I have to Use the discriminate to determine the number of values of w in the equation from part (a). I can do that and part c. Many thanks for your help!!!

• Geometry / Algebra 1 -

surface area=2ab+2bc+2ac
I will surmise the you have a rectangular prism.

surface area=2ab+2bc+2ac
= 2(wm)(8m) + 2(8m)(w+4) + 2(wm)(W+4) = 314
16 wm^2 + 16wm + 64m + 2mw^2 + 8wm = 314

Since we want to solve for w, let's consider this to be a quadratic equation in w

2m w^2 + w(16m^2 + 16m + 8m) + 64m - 314 = 0
so comparing this to ax^2 + bx + c = 0
a = 2m , b = (16m^2 + 24m) , and c = 64m-314

the discriminant = b^2 - 4ac
= ...

you said you could do that.

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