Hey guys, wondering how to solve B and C. In Greg’s prepswift the angle within the parallelogram is also given. However, we only have the 90 degree angle in the right triangle that has been used to find the height.
B: We need to figure out the lengths of all 4 sides
In parallelograms, opposite sides are congruent, so we only need to know 2 lengths
We know AD is 12 so BC is also 12
DC = the hypotenuse of the dotted line triangle, so use pythagorean theorem to solve.
Once we know DC, we can add up all 4 sides to get the perimeter (DC = AB)
C: Length of BD:
BD is a diagonal connecting B and D. How can we find the length?
In these scenarios, try to draw imaginary lines to make situations where you can solve for a length. Often that means trying to find some right triangles where you know 2 side lengths.
Here, draw a line from point D perpendicular to the opposite side (BC). Lets call the intersection of that line on BC, point X. So, now we have a right triangle DXB.
If we can find the length of DX and XB, we can solve for the hypotenuse BD.
Notice that DX = 4, because of the given side length of the dotted line triangle
Notice that XB = BC - 2, again from the dotted line triangle. So XB = 12-2 = 10.
Now we have 2 sides of a right triangle. Use pythagorean theorem to solve for BD, which is the answer to question C).
