Answer:
The possible lengths of the third side is all real numbers greater than 4 inches and less than 20 inches
Step-by-step explanation:
we know that
<u>The Triangle Inequality Theorem</u>. states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side
Let
x -----> the possible lengths of the third side
Applying the Inequality Theorem
1) 12+8 > x
20 > x
Rewrite
x < 20 in
2) 8+x > 12
x> 12-8
x > 4 in
therefore
4 in < x < 20 in
The possible lengths of the third side is all real numbers greater than 4 inches and less than 20 inches
Answer:
187 cm²
Step-by-step explanation:
The bottom rectangle area is easy, it is 15*9 = 135 cm².
To find the area of the triangle, you only need the base width and its height (you don't need the hypotenuse). You can then use the formula: area triangle is base times half height.
The base width is 15-7 = 8 cm
The height is 22-9 = 13 cm
So the area of the triangle is 13*8/2 = 52 cm²
Together with the 135 of the rectangle that sums to 52+135 = 187 cm².
Hi!
This is definitely a trapezoid, as it has two equal sides and two inequal sides. It's not a parallelogram, because two sides eventually intersect. It is a quadrilateral, because it has four sides.
None of the others apply here.
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<span>a I took the test on ingenuity</span>
The expression that expresses all possible lengths of segment AB is 27 < AB < 81. The correct option is the second option 27 < AB < 81
<h3>Properties of a triangle</h3>
From the question, we are to determine the expression that expresses all possible lengths of segment AB
From one of the properties of a triangle,
The <u>third side</u> of any triangle is greater than the difference of the other <u>two sides</u>; and the <u>third side</u> of any triangle is lesser than the sum of the <u>two other sides</u>
Then, we can write that
AB < 27 + 54
and
AB > 54 - 27
Putting the two inequalities together, we get
54 - 27 < AB < 27 + 54
27 < AB < 81
Hence, the expression that expresses all possible lengths of segment AB is 27 < AB < 81. The correct option is the second option 27 < AB < 81
Learn more on the Properties of a triangle here: brainly.com/question/1851668
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