Find the area of each isosceles triangle . Show work ! ### Geometry Problem: Triangle Dimensions**Problem 9:**The diagram above showcases a triangle with the following dimensions:- The two sides of the triangle, which are both equal, each measure 51 meters.- The base of the triangle is 48 meters.- An internal vertical line segment, labeled $ h $, represents the height from the base to the top vertex, dividing the triangle into two right-angled triangles.The geometric figure can be used to calculate various properties of the triangle, such as the height $ h $ using the Pythagorean theorem.#### Diagram Explanation:- The triangle is isosceles, having two equal sides.- The height $ h $ creates two congruent right-angled triangles.- The base of the right-angled triangles is $ 24 $ meters (half of 48 meters).To find the height $ h $, you can use the Pythagorean theorem:\[ h = \sqrt{51^2 - 24^2} \]Use this approach to solve for $ h $.

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Answered: 9) 51 m 51 m 48 m

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Find the area of each isosceles triangle . Show work !

### Geometry Problem: Triangle Dimensions

**Problem 9:**

The diagram above showcases a triangle with the following dimensions:

- The two sides of the triangle, which are both equal, each measure 51 meters.
- The base of the triangle is 48 meters.
- An internal vertical line segment, labeled $ h $, represents the height from the base to the top vertex, dividing the triangle into two right-angled triangles.

The geometric figure can be used to calculate various properties of the triangle, such as the height $ h $ using the Pythagorean theorem.

#### Diagram Explanation:
- The triangle is isosceles, having two equal sides.
- The height $ h $ creates two congruent right-angled triangles.
- The base of the right-angled triangles is $ 24 $ meters (half of 48 meters).

To find the height $ h $, you can use the Pythagorean theorem:

\[ h = \sqrt{51^2 - 24^2} \]

Use this approach to solve for $ h $.

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

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