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Naddika [18.5K]
3 years ago
6

The height of a triangle is 4 times its base. The area of the triangle is 288 square. Find the base and the height of the triang

le
Mathematics
1 answer:
Vanyuwa [196]3 years ago
7 0
\bf \textit{area of a triangle}\\\\
A=\cfrac{1}{2}bh\qquad 
\begin{cases}
b=base\\
h=height\\
----------\\
h=4b\leftarrow 
\begin{array}{llll}
\textit{height is 4}\\
\textit{times the base}
\end{array}\\
A=288
\end{cases}\implies 288=\cfrac{1}{2}\cdot b\cdot 2b

solve for "b", to see what the base is

what about the height?  well, h = 4b
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(-3/2)x - 9 = - 27 solve for x
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Answer:

x = 12

Step-by-step explanation:

Solve for x:

(-3 x)/2 - 9 = -27

Put each term in (-3 x)/2 - 9 over the common denominator 2: (-3 x)/2 - 9 = (-18)/2 - (3 x)/2:

(-18)/2 - (3 x)/2 = -27

(-18)/2 - (3 x)/2 = (-3 x - 18)/2:

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Multiply both sides of (-3 x - 18)/2 = -27 by 2:

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(2 (-3 x - 18))/2 = 2/2×(-3 x - 18) = -3 x - 18:

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Add 18 to both sides:

(18 - 18) - 3 x = 18 - 54

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Divide both sides of -3 x = -36 by -3:

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x = (-36)/(-3)

The gcd of -36 and -3 is -3, so (-36)/(-3) = (-3×12)/(-3×1) = (-3)/(-3)×12 = 12:

Answer:  x = 12

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