In order to begin we must start off with the formula for the area of a triangle, which is a=1/2b(h) where a is area, b is base, and h is height.
In this scenario, we know that the area is 45cm^2 and the base is 2h+12 (since it is twice it’s height plus twelve). We can plug this into the area equation and then proceed to solve out accordingly.
a=1/2b(h)
45=1/2(2h+12)(h)
90=(2h+12)(h)
90=2h^2 + 12h
0= 2h^2 + 12h - 90
Simplify by dividing the two out.
h^2 + 6h - 45 = 0.
Now plug into the quadratic formula (with a=1, b=6, and c=-45) as shown in the image below.
After plugging the equation in and solving, we come to the idea that h is roughly equal to 4.34. We can now plug this back into the triangle area formula to solve out for b.
a=1/2b(h)
45=1/2(2h + 12)(h)
45=1/2(20.69)(4.34)
45=45.
In conclusion;
The height is ≈ 4.34
The base is ≈ 8.68
Hope this helps :)
Answer:
d=5
Step-by-step explanation:
Without speeding up it would take 5 1/3 seconds.. not sure if it speeds up in the question?
Answer:
Try Khan Academy. They give lots of expression to find the greatest difference. It always helps me in this situation.
Step-by-step explanation:
Answer:
km
Step-by-step explanation:
The submarine's path from its base forms a right triangle when its final position is "connected" to the base. We know that the right triangle has legs of 
km and 
km, and we need to find the length of its hypotenuse. To do so, we can use the Pythagorean Theorem, which states that in a right triangle, 
, where 
and 
are the lengths of the triangle's legs and 
is the length of the triangle's hypotenuse. In this case, we know what and are, and we need to solve for c, so after substituting the given values of and into to solve for c, we get:
(Substitute 
and 
into the equation)
(Evaluate the squares on the LHS)
(Simplify the LHS)
(Symmetric Property of Equality)
(Take the square root of both sides of the equation)
(Simplify)
is an extraneous solution because you can't have negative distance, if that makes sense, so therefore, the submarine is approximately km away from its base. Hope this helps!
