Estimated Time: 25–30 minutes
Group Size: 2
Right
Right triangles have an important property that the sum of the squares of the two legs of a right triangles have an important property that the sum of the squares of the two legs of a right triangle equals the square of the hypotenuse. This fact is referred to as the Pythagorean theorem. In symbols, the Pythagorean theorem is stated as:
Now equate the two expressions representing the area of the large outer square:
To calculate: The expression representing the area of large outer square. The figure is as follows:
Answer to Problem 3GA
Solution:
Equating the area of large outer square to the sum of area of Inner Square and area of four right triangle gives
Explanation of Solution
Given Information:
The area of Inner Square is
Formula Used:
The area of square is
The area of right-angle triangle is
Calculation:
Consider the given figure.
Steps to determine the area of large outer square:
Step1: First determine the area of Inner Square and area of four right triangles.
Step2: Then add both areas which is equal to area of large outer square.
Area of Inner Square is
Now, add these two areas and equate it to the area of large outer square.
Clear the parenthesis on both sides of the equation.
Subtract
Thus, equating the area of large outer square to the sum of area of Inner Square and area of four right triangle gives
Want to see more full solutions like this?
Chapter 5 Solutions
Beginning and Intermediate Algebra
- Write three of the properties of triangles from this section and then explain each in your own words.arrow_forwardIn right triangle ABC,CD- is the altitude from C to hypotenuse AB-. Name three triangles that are similar to each other.arrow_forwardOne angle of a right triangle measures 45°. What is the measure of the other small angle?arrow_forward
- a To locate the orthocenter, is it necessary to construct all three altitude of a right triangle? b What point is the orthocenter of any right triangle?arrow_forwardSquare RSTV has diagonals RT and SV not shown. If the diagonals are drawn, how will their lengths compare? Do the diagonals of a square appear to be perpendicular?arrow_forwardABC is similar to XYZ The lengths of two sides of each triangle are given in the figure. Find the length of side a.arrow_forward
- Gina is standing near a building and notices that the angle of elevation to the top of the building is 68. She then walks 72 feet further away from the building and notices that the angle of elevation to the top of the building is now only 51. Find the height of the building. a. 2511 b. 56ft c. 149ft d. l80ftarrow_forwardThe imaginary number i has the property that i2 = ___________________ .arrow_forward
- Trigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage LearningHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALElementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage LearningIntermediate AlgebraAlgebraISBN:9781285195728Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage Learning