Page 162 - Math Course 2 (Book 1)

Radical Expressions: Pythagorean Theorem

Let’s Begin

Pythagorean Triples Check for Right Triangles

Example Examples

What is the area of triangle XYZ? Z Determine whether the side measures of 7, 12, 15
form a right triangle.
A. 94 units 2
B. 128 units 2 35 Since the measure of the longest side is 15,
2
C. 294 units let c = 15, a = 7, and b = 12. Then determine
2
2
2
D. 588 units 2 whether c = a + b .
X 28 Y
2
2
c = a + b 2 Pythagorean Theorem
Read the Test Item
1 2 2 2
. In a right
The area of the triangle is A = bh 15 = 7 + 12 a = 7, b = 12, and c = 15
2
triangle, the legs from the base and height of the
225 = 49 + 144 Multiply.
triangle. Use the measures of hypotenuse and the
base to f nd the height of the triangle. 225 ≠ 193 Add.
Solve the Test Item Since c ≠ a + b , the triangle is
2
2
2
Answer
Step 1 Check to see if the measurements of not a right triangle.
this triangle are a multiple of a common
Pythagorean triple. The hypotenuse is
7 • 5 units and the leg is 7 • 4 units. This Determine whether the side measures of 27, 36, 45
triangle is a multiple of a (3, 4, 5) triangle. form a right triangle.
7 • 3 = 21 Since the measure of the longest side is 45,
7 • 4 = 28 let c = 45, a = 27, and b = 36. Then determine
2
2
2
7 • 5 = 35 whether c = a + b .
2
2
2
The height of the triangle is 21 units. c = a + b Pythagorean Theorem
Step 2 Find the area of the triangle. 45 = 27 + 36 a = 27, b = 36, and c = 45
2
2
2
1 2025 = 729 + 1296 Multiply.
A = bh
2 Area of a triangle
2025 = 2025 Add.
1
A = (28)(21) b = 28 and h = 21
2
2
2
2 Since c = a + b , the triangle
Answer
is a right triangle.
A = 294 Simplify.
The area of the triangle is 294
Answer
square units. Choice C is correct.

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