An altitude is drawn from the vertex of an isosceles triangle, forming a right angle and two congruent triangles. As a result, the altitude cuts the base into two equal segments. The length of the altitude is 5 inches, and the length of the base is 2 inches. Find the triangle’s perimeter. Round to the nearest tenth of an inch.

In an isosceles triangle with an altitude drawn from the vertex, it creates two congruent right-angled triangles. This altitude also bisects the base into two equal segments.

Let's denote the length of one of the congruent segments of the base as x Since the entire base is 2 inches, each segment is x = 2}{2} = 1 inch.

Now, using the Pythagorean theorem in one of the right-angled triangles:

a^2 + b^2 = c^2

where a and b are the legs of the right triangle, and c is the hypotenuse (the altitude in this case).

Let's use a = b = 1 in

ch and c = 5 inches:

1^2 + 1^2 = 5^2

2 = 25

This is not true, so there seems to be an issue.

Please double-check the provided information, as the values given for the base length and altitude might not be correct

sqdancefan sqdancefan · Answer 2 · 2024-01-14T20:52:50+01:00

Answer:

12.2 inches

Step-by-step explanation:

You want the perimeter of an isosceles triangle with base 2 inches and altitude 5 inches.

Side length

The length of one side of the triangle is given by the Pythagorean theorem:

c = √(a² +b²)

c = √(1² +5²) = √26

The two sides are the same length. When added to the base, they give the perimeter as ...

P = 2a +2c = 2(1) +2√26) ≈ 12.2 . . . . inches

The triangle's perimeter is about 12.2 inches.

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Additional comment

Here, we have used a=1, half the length of the base, and b=5, the altitude. The hypotenuse of the right triangle formed by the altitude and half the base is c=√26. This is different from the usual definitions of a, b, c as sides opposite angles A, B, C. Do not be confused.