If a triangle has base 6 and height 4, and both base and height are doubled, by what factor does the area increase?

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Multiple Choice

If a triangle has base 6 and height 4, and both base and height are doubled, by what factor does the area increase?

Doubling both the base and the height multiplies the area by 4 because the area of a triangle is (1/2) times base times height, so increasing each dimension by a factor of 2 makes the product base × height increase by 2 × 2 = 4. With original base 6 and height 4, the area is (1/2) × 6 × 4 = 12. After doubling, the base is 12 and the height is 8, so the area is (1/2) × 12 × 8 = 48, which is four times the original.

Doubling both the base and the height multiplies the area by 4 because the area of a triangle is (1/2) times base times height, so increasing each dimension by a factor of 2 makes the product base × height increase by 2 × 2 = 4. With original base 6 and height 4, the area is (1/2) × 6 × 4 = 12. After doubling, the base is 12 and the height is 8, so the area is (1/2) × 12 × 8 = 48, which is four times the original.

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