Answer:
10.2
Explanation:
You want the perimeter of an isosceles right triangle with a leg length of 3.
Isosceles right triangle
An isosceles right triangle with a leg length of 1 has a hypotenuse (c) given by ...
c² = a² +b² . . . . . . where 'a' and 'b' are the leg lengths
c² = 1² + 1² = 2
c = √2
That is, the ratios of the lengths of the sides in an isosceles right triangle is ...
1 : 1 : √2
Perimeter
The sum of the lengths of these sides is ...
1 + 1 + √2 ≈ 3.4142
The given triangle is scaled up from this by a factor of 3, so its perimeter is ...
P = 3×3.4142 ≈ 10.2 . . . . units
The perimeter of the triangle is about 10.2 units.
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Additional comment
It is worthwhile to remember the relationship between side lengths for this "special" right triangle. You will see it again.
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