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The area of a triangle is 1,440 cm². The base of the triangle is 5 times the height. What is the height of the triangle?
O 12 cm
O 24 cm
O 46 cm
O 60 cm
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Verified Answer :

GinnyAnswer

To solve this problem, we will use the formula for the area of a triangle, which is:

\(\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]\)

Since we're given that the area of the triangle is 1,440 cm² and that the base is 5 times the height, we can set our variables as follows:

Let \(\( h \)\) be the height of the triangle.
Therefore, the base \(\( b \)\) of the triangle is \(\( 5h \)\).

We can now express the area in terms of \(\( h \)\):

\(\[ 1440 = \frac{1}{2} \times (5h) \times h \]\)

Now we simplify and solve for \(\( h \)\):

\(\[ 1440 = \frac{1}{2} \times 5h^2 \]\)
\(\[ 1440 = \frac{5}{2}h^2 \]\)

Multiply both sides by 2 to get rid of the fraction:

\(\[ 1440 \times 2 = 5h^2 \]\)
\(\[ 2880 = 5h^2 \]\)

Now divide both sides by 5:

\(\[ \frac{2880}{5} = h^2 \]\)
\(\[ 576 = h^2 \]\)

To find \(\( h \)\), we take the square root of both sides:

\(\[ h = \sqrt{576} \]\)

The square root of 576 is 24. Therefore:

\(\[ h = 24 \text{ cm} \]\)

The height of the triangle is 24 cm.

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