Answer:
8 cm
Explanation:
You want the base of a triangle, given its height is 3 cm. From the base of 12 cm, the same triangle has a height of 2 cm.
Area
The area of a triangle is given by the formula ...
A = 1/2bh
The area will be the same for any (base, height) pair of dimensions. The height is always measured perpendicular to the base. The base is generally one side of the triangle.
Application
Here, the longest side is labeled 12 cm, and the perpendicular distance to the opposite vertex (height) is labeled 2 cm. This means the triangle area is ...
A = (1/2)(12 cm)(2 cm) = 12 cm²
The distance perpendicular to the unknown side is shown as 3 cm. This gives you a clue that using the area of the triangle to find the unknown side is probably useful.
A = 1/2bh
12 cm² = 1/2(b)(3 cm)
8 cm = b . . . . . . . . . . . . multiply by 2/(3 cm)
The value that goes in the box is 8.
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Additional comment
The attachment is drawn to scale.
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