Question

The area of a triangle is 1440 cm^2. The base of the triangle is 5 times the height. What is the height of the triangle

Answer 1

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Formula
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Area of triangle = 1/2 x base x height

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Define base and height
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Let the height be x
height = x
base = 5x

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Find Height
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`1440 = (1)/(2) (x)(5x)`


`1440 = (5)/(2) x^2`


`x^2 = 1440 / (5)/(2)`


`x^2 = 1440 * (2)/(5)`


`x^2 = 576`


`x = √(576)`


`x = 24`

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Find base and Height
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height = x = 24 cm
base = 5x = 24 x 5 = 120 cm

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Answer: Height = 24cm
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Answer 2

To find the area of a triangle you would use this formula: bh/2 = Area.
If the base is 5 times the height, then 46 wouldn't be the answer.
That would be: 46 x 230 = 10,580
10,580/2 = 5,290 which isn't 1,440.
However if it was 24 we get this: 24 x 5 = 120
24 x 120 = 2,880
2,880/2 = 1,440.
So the answer is: 24cm