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miv72 [106K]
2 years ago
8

In \triangle LMN,△LMN, \angle N \cong \angle M,∠N≅∠M, LM = 14LM=14 and MN = 8MN=8. Find the length of NL.NL.

Mathematics
1 answer:
Black_prince [1.1K]2 years ago
7 0

Answer:

11.5

Step-by-step explanation:

We solve using :

Pythagoras Theorem

LM² = MN² + NL²

NL² = LM² - MN²

NL = √LM² - MN²

NL = √14² - 8²

NL =  √(132)

NL = 11.489125293

NL = 11.5

Therefore, the length of NL = 11.5

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The correct answer is:  [B]:  "40 yd² " .
_____________________________________________________
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The formula of the area of a triangle, "A":

A = (1/2) * b * h ; 

in which:  " A = area (in units 'squared') ;  in our case, " yd² " ; 

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→  A = (1/2) * b * h = (1/2) * (6 yd) * (8 yd) = (1/2) * (6) * (8) * (yd²) ; 
                                                                 
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Now, find the area, "A", of the square:

The formula for the area, "A" of a square:

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Now, we add the areas of BOTH the triangle AND the square:
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        →  " 24 yd²  +  16 yd² " ; 

to get:  " 40 yd² " ;  which is:  Answer choice:  [B]:  " 40 yd² " .
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