A box has a total surface area of 100. The length of the box is equal to twice its width, as well as equal to 3 less than its height. What is the height of the box?

Question

Angle · Answer

L = 2W
L = H - 3

SA = L x W x H

Angle · Answer

uhh

W = 0.5 L
H = L + 3
?

so
SA = L x (0.5 L) x (L + 3)

Vocaloid · Answer

That’s volume not surface area

2LW + 2WH + 2LH

Angle · Answer

ahhh shoot

Angle · Answer

rip

Angle · Answer

thanks voca

Vol = 2LW + 2WH + 2LH
Vol = 2(L)(0.5L) + 2(0.5L)(L+3) + 2(L)(L+3)
      = L^2 + L^2 + 3L + 2L^2 + 6L
      = 4L^2 + 9L

Angle · Answer

100  =  4L^2 + 9L

4L^2 + 9L - 100 = 0

hmm

Angle · Answer

400 = 25x16

4L^2 - 16L + 25L - 100 = 0

4L(L - 4) + 25(L - 4) = 0

(L - 4) (4L + 25) = 0

L = 4
&
L = -25/4

Angle · Answer

Length can't be negative so L = 4

then since H = L + 3
H = 4 + 3 = 7

Angle · Answer

eh good enough