Question

HELP! I don't understand so please give a detailed explanation.

Answer 1

From the picture, we can see that ΔLSP and ΔLRN are similar, so corresponding sides are proportionate:

LN : LP = 28:12 = 7:3

Therefore, the LRN sides is 7/3 of the corresponding side of LSP.

Then, it states that the area of LSP = 50, and area of a triangle is (1/2)bh, so we set up the equation

Area of LSP = (1/2)bh = 50 ← Remember how the corresponding sides are 7/3 of LSP? Therefore, the area of LRN:

LRN = (1/2)(7b/3)(7h/3) ← Take out the 7/3 and multiply them together

= (49/9)(1/2)bh ← From LSP, we know that (1/2)bh = 50, so plug that in

= (49/9)*50 ≈ 272.222 units ²