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Math

QuestionA triangle has sides of 6 in and 26 in. Find the area of a similar triangle with sides half the length of the original.

Studdy Solution

STEP 1

Assumptions1. The original triangle has two sides that measure6 inches and26 inches. . The smaller triangle is similar to the original triangle, meaning it has the same shape but different size.
3. The sides of the smaller triangle are exactly half the length of the corresponding sides of the original triangle.

STEP 2

The area of a triangle is given by the formulaArea=12×base×heightArea = \frac{1}{2} \times base \times height

STEP 3

Assuming the two given sides (6 inches and26 inches) are the base and the height of the original triangle, the area of the original triangle isAreaoriginal=12×6 inches×26 inchesArea_{original} = \frac{1}{2} \times6 \, inches \times26 \, inches

STEP 4

Calculate the area of the original triangle.
Areaoriginal=12×6 inches×26 inches=78 square inchesArea_{original} = \frac{1}{2} \times6 \, inches \times26 \, inches =78 \, square \, inches

STEP 5

The sides of the smaller triangle are half the length of the corresponding sides of the original triangle. Therefore, the base and the height of the smaller triangle are3 inches and13 inches, respectively.

STEP 6

The area of the smaller triangle isAreasmaller=12×3 inches×13 inchesArea_{smaller} = \frac{1}{2} \times3 \, inches \times13 \, inches

STEP 7

Calculate the area of the smaller triangle.
Areasmaller=12×3 inches×13 inches=19.5 square inchesArea_{smaller} = \frac{1}{2} \times3 \, inches \times13 \, inches =19.5 \, square \, inchesThe greatest possible area of the smaller triangle is19.5 square inches.

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