Question

Find the perimeter of the isosceles triangle in feet. If needed, please round to the nearest tenth.

triangle with height of 7 and base of 48 feet. tick marks on two sides



Only 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, . , -, and / are allowed in your answer. Answers that are mixed numbers must be entered as an improper fraction or decimal.

Answer 1

To find the perimeter of the isosceles triangle, we need to calculate the lengths of the two equal sides and then add them to the base length.

Given:
- Height (h) = 7 feet
- Base (b) = 48 feet

Since the triangle is isosceles, we can split it into two right triangles by drawing a line from the apex (top point of the triangle) down to the midpoint of the base. This creates two right triangles with the following dimensions:

- Base of each right triangle = \( \frac{b}{2} = \frac{48}{2} = 24 \) feet
- Height = 7 feet

Now, we can use the Pythagorean theorem to find the length of one of the equal sides (let's call it \( l \)):

\[
l^2 = \text{(height)}^2 + \text{(half the base)}^2
\]
\[
l^2 = 7^2 + 24^2
\]
\[
l^2 = 49 + 576
\]
\[
l^2 = 625
\]
\[
l = \sqrt{625} = 25 \text{ feet}
\]

Now, we know the lengths of all sides:
- Two equal sides = \( 25 \) feet each
- Base = \( 48 \) feet

Now, we can calculate the perimeter \( P \):

\[
P = 2l + b = 2(25) + 48
\]
\[
P = 50 + 48 = 98 \text{ feet}
\]

Thus, the perimeter of the isosceles triangle is **98 feet**.