Answer:
Alternate-exterior angles theorem.
Step-by-step explanation:
Two parallel lines are cut by a transversal, and if there are a pair of congruent angles that are outside of the parallel lines, and on opposite sides of the transversal, you will have the alternate-exterior angles theorem.
The length of pencil A is 5 cm
<em><u>Solution:</u></em>
Let the length of pencil A be "x"
Let the length of pencil B be "y"
Let the length of pencil C be "z"
<em><u>The total length of pencils A, B and C is 29 cm</u></em>
Therefore,
length of pencil A + length of pencil B + length of pencil C = 29
x + y + z = 29 ------------ eqn 1
<em><u>Pencil A is 11 cm shorter then pencil B</u></em>
x = y - 11 ------- eqn 2
<em><u>Pencil B is twice as long a pencil C</u></em>
y = 2z
------ eqn 3
<em><u>Substitute eqn 2 and eqn 3 in eqn 1</u></em>

<em><u>Substitute y = 16 in eqn 2</u></em>
x = 16 - 11
x = 5
Thus length of pencil A is 5 cm
Answer:
11,448 in²
Step-by-step explanation:
The area can be computed from ...
... A = 2(LW +H(L+W))
For the given prism, the area will be ...
... A = 2(18·12 +14(18+12)) = 2(216 +420) = 1272 . . . . in²
The area of a similar figure with dimensions 3 times as long will be 3² times as much. The area of the new figure is ...
... A = 3²×(1272 in²) = 11,448 in²