a.
To calculate: Thelength of CD
a.
Answer to Problem 3PSA
The length of CD is
Explanation of Solution
Given:
The measures of the given lengths are as follows:
AD =
BD =
Concept used:
Here, we are using the concept hypotenuse leg theorem.
Calculation:
According to property associated with altitudes in right
Hence,
So,
→
→
→
Conclusion: Hence, the length of CD is
b.
To calculate: Thelength of AC
b.
Answer to Problem 3PSA
The length of AC is
Explanation of Solution
Given:
The measures of given lengths are as follows:
AD =
AB =
Formula used:
Here, we are using Pythagoras theorem
Calculation: According to property associated with altitudes in right angled triangle. The altitude to hypotenuse divides the triangles into two similar triangles.
Hence,
So,
Here, AD =
So,
And,
Conclusion: Hence, the length of AC is
c.
To calculate: Thelength of BC
c.
Answer to Problem 3PSA
The length of BC is
Explanation of Solution
Given:
The measures of the given lengths are as follows:
BD =
AB =
Concept used:
Here, we are using the concept hypotenuse leg theorem.
Calculation:
According to property associated with altitudes in right angled triangle. The altitude to hypotenuse divides the triangles into two similar triangles.
Hence,
So,
And,
Conclusion: Hence, the length of BC is
d.
To calculate: Thelength of AD
d.
Answer to Problem 3PSA
The length of ADis
Explanation of Solution
Given:
The measures of the given lengths are as follows:
CD =
BD =
Concept used:
Here, we are using the concept hypotenuse leg theorem.
Calculation:
According to property associated with altitudes in right angled triangle. The altitude to hypotenuse divides the triangles into two similar triangles.
Hence,
So,
Conclusion: Hence, the length of AD is
e.
To calculate: Thelength of AC
e.
Answer to Problem 3PSA
The length of AC is
Explanation of Solution
Given: The measures of the given lengths are as follows:
AD =
BD =
Concept used:
Here, we are using the concept hypotenuse leg theorem.
Calculation:
According to property associated with altitudes in right angled triangle. The altitude to hypotenuse divides the triangles into two similar triangles.
Hence,
So,
Conclusion: Hence, the length of AC is
f.
To calculate: Thelength of AB
f.
Explanation of Solution
Given:
The measures of the given lengths are as follows:
BC =
BD =
Concept used:
Here, we are using the Pythagoras theorem.
Calculation:
Here,
Here, the value of CD will be negative which is not possible.
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- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning