LCM stands for least common multiple, and so the LCM of two number is the smallest possible common multiple of the two numbers.
Since 16 is already a multiple of 8 (and since every number is a multiple of itself), the LCM between 8 and 16 is sixteen itself: it is a multiple of 8, it is a multiple of 16, and there couldn't be a smaller one.
Even though this case was trivial, let's do the computation to learn how to do this in general: first of all, you need the prime factorizations of the two numbers:
The LCM of the two numbers is composed by all the primes appearing in any of the two factorizations. In case a prime appears in both factorizations, we choose the one with higher exponents.
In this case, 2 is the only prime to appear in both factorizations. So, we choose the one with higher exponent, which is 4, and the answer is 
, as we already observed.
Complementary angles have a sum of 90°
Supplementary angles have a sum of 180°
So
∠b=90-a=90-38=52°
∠c=180-b=180-52=128°
Let h represent the height. Then the base is h+6 (all measurements are in feet).
The formula for the area of a triangle is A = (base)(height)/2.
Here A = 114 ft^2 = (base)(height)/2. Substituting the (h+6) and h,
A = [114 ft^2] = [(h+6)(h)]/2 , or [h^2 + 6h]/2, or 2A = 228 = (h+6)h. Multiply out the right side
Solve 228 = h^2 + 6h for h:
h^2 + 6h - 228 = 0
Applying the Quadratic Formula,
-6 plus or minus sqrt(36-4(1)(-228))
h = -------------------------------------------------
2
-6 plus or minus sqrt(948) -6 plus or minus 30.79
or h = ------------------------------------- = ------------------------------------ 2 2
-6 plus or minus 30.79
h = ----------------------------------
2
We want only the positive result. That comes to h = 30.79-6
----------
2
or 24.79/2, or h = 12. 40
h represents the altitude of the triangle, so h+7 represents the length of the base. These values are 12.40 feet and 19.40 feet respectively.
Substitute b=19.40 feet and h=12.40 feet into the formula A = bh/2.
Is the result 114 sq. ft. ?
Step-by-step explanation:
I'd 5261333821 . p. 12345 on z.o.o.m
