Answer :
Problem 1
Answer: AD = 9
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Work Shown:
Focus on triangle ADB, which is the smaller triangle on the left.
We have these side lengths
AD = unknown leg
BD = 12 = known leg
AB = 15 = known hypotenuse
Let's apply the Pythagorean Theorem to find the unknown leg
a^2 + b^2 = c^2
(AD)^2 + (BD)^2 = (AB)^2
(AD)^2 + (12)^2 = (15)^2
(AD)^2 + 144 = 225
(AD)^2 = 225-144
(AD)^2 = 81
AD = sqrt(81)
AD = 9
Side AD is 9 units long.
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Problem 2
Answer: AC = 25
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Work Shown:
AC = AD + DC .... segment addition postulate
AC = 9 + 16 ..... substitution; refer to problem 1
AC = 25
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Problem 3
Answer: Triangle ABC is a right triangle.
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Work Shown:
The Pythagorean Theorem Converse says "if a^2+b^2 = c^2 is a true equation, then the triangle with sides a,b,c is a right triangle". Keep in mind that c is always the longest side (hypotenuse). The order of 'a' and b doesn't matter. Convention has us usually do [tex]a \le b[/tex] but again the order isn't important.
We have these three sides
- a = 15 (length of side AB; leg #1)
- b = 20 (length of BC; leg #2)
- c = 25 (length of AC; hypotenuse)
Plug those values into the equation below. Simplify each side.
a^2+b^2 = c^2
15^2 + 20^2 = 25^2
225 + 400 = 625
625 = 625
We get a true equation. Therefore, triangle ABC is a right triangle.
Answer:
Step-by-step explanation:
Pythagorean = c^2 =a^2 + b^2
we are given c and a so solve for b
c^-a^2 = b^2
15^2- 12^ = b^2
81= b^2
[tex]\sqrt{81}[/tex]=b
9=b
AD=b
AC = AD + 16
AC =9 + 16 =25
if it's a right triangle then Pythagorean will work with the sides to make 25
AC^2 = 15^2+20^2
AC = [tex]\sqrt{625}[/tex]
AC = 25