To begin, we calculate the length of the hypotenuse of a triangle by applying the Pythagorean theorem formula: c^2 = a^2 + b^2, where c represents the hypotenuse, and a and b are the lengths of the other two sides. Substituting the values given, we find that c^2 = 4^2 + 7^2, which simplifies to c^2 = 16 + 49, resulting in c^2 = 65 and c = √65, which is approximately 8.1 inches.
Following this, we determine the area of the triangle using the formula: Area = 0.5 * base * height. Plugging in the base length of 4 inches and the height of 7 inches, we calculate the area to be 0.5 * 4 * 7, which equals 14 square inches.
In conclusion, the area of the triangle with a hypotenuse measuring approximately 8.1 inches, a shorter side of 4 inches, and a longer side of 7 inches is estimated to be 14 square inches.
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First, we need to find the length of the hypotenuse using the Pythagorean theorem:
c^2 = a^2 + b^2
where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.
c^2 = 4^2 + 7^2
c^2 = 16 + 49
c^2 = 65
c = √65
c ≈ 8.1 inches
Next, we can find the area of the triangle using the formula:
Area = 0.5 * base * height
Area = 0.5 * 4 * 7
Area = 14 square inches
Therefore, the area of the triangle with a hypotenuse of 8.1 inches, a smaller side of 4 inches, and a bigger side of 7 inches is approximately 14 square inches.
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