Question

I need help with all of them please help me

Answer 1

`\begin{gathered} a)198in^(2) \\ b)3 \\ c)x=6 \end{gathered}`

1) We can see here the net surface of that gingerbread house, so we need to find the area of the 4 triangles and the rectangle. So we can write out:

a)

`\begin{gathered} A_(\Delta)=(b\cdot h)/(2) \\ 2A_(\Delta)=2((b\cdot h)/(2))=2((6\cdot8)/(2))=48in^(2) \\ A_R=12\cdot8=96in^(2) \\ 2A_(\Delta)=2((4.5\cdot12)/(2))=54in^(2) \\ A_H=54+96+48 \\ A_H=198in^(2) \end{gathered}`

Note that not all triangles are congruent to each other, so we needed to do it separately.

b) We can find the number of batches by setting a direct proportion:

`\begin{gathered} 1----50in^(2) \\ x----198in^(2) \\ x=(198)/(50)=3.96 \end{gathered}`

We can count batches with whole numbers and despite 3.96 is almost 4 we can tell that the answer is 3 batches

c) Since Wendy wants a Gingerbread house twice as much, and we can see rectangles we can write out the following equation:

`\begin{gathered} (12\cdot7)+(12\cdot7)+12x+12x+7x+7x=2\cdot198 \\ 12\cdot\: 7+12\cdot\: 7+12x+12x+7x+7x=2\cdot\: 198 \\ 12\cdot\: 7+12\cdot\: 7+38x=2\cdot\: 198 \\ 2\cdot\: 12\cdot\: 7+38x=2\cdot\: 198 \\ 168+38x=2\cdot\: 198 \\ 168+38x=396 \\ 168+38x-168=396-168 \\ 38x=228 \\ (38x)/(38)=(228)/(38) \\ x=6 \end{gathered}`

And that is the missing side.