Question

The base of a triangle is 4 cm greater than the height. the area is 48 cm squared. find the height and base of the triangle.

Answer 1

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Given information
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Area of the triangle = 48 cm²
The base is 4 cm greater than the height

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Define height and base
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Let height be x
height = x
base = x + 4

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

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Substitute x and solve
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1/2(x+4)(x) = 48
1/2 (x² + 4x) = 48
x² + 4x = 48 x 2
x² + 4x - 96 = 0
(x - 8)(x + 12) = 0
 x = 8 or x = 12 (rejected, length cannot be negative)

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Find base and height
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Height = x = 8cm
base = x + 4 = 8 + 4 = 12cm

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Answer: The height is 8cm and the base is 12 cm
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