Answer:
B. 642.22 units squared
Step-by-step explanation:
Knowing that QP ║ MN and ∠QLP = ∠MLN, then ΔQLP ~ ΔMLN.
That means corresponding sides and heights have the same ratios.
We know that QP = 25, which corresponds to MN = 34. Also, the height of ΔQLP, LS, corresponds to the height of ΔMLN, LR = LS + SR = LS + 10. Let's say LS = x.
We can now write:
QP / MN = LS / LR
25 / 34 = x / (x + 10)
Cross-multiply:
34 * x = 25 * (x + 10)
34x = 25x + 250
34x - 25x = 250
9x = 250
x = 250/9 ≈ 27.78 units
So, LS = 27.78 units and LR = LS + SR = 27.78 + 10 = 37.78 units.
The area of a triangle is denoted by A = (1/2) * b * h, where b is the base and h is the height.
Here, the base of ΔLMN is MN = 34, and the height is LR = 37.78. Plug these in:
A = (1/2) * b * h
A = (1/2) * 34 * 37.78 ≈ 642.22 units squared
The answer is thus B.
<em>~ an aesthetics lover</em>
