A triangle has sides of lengths 5 cm, 5 cm, and square root 47cm.
Which of the following statements is true?
A. The triangle is an obtuse triangle because (√47)^2>5^2+5^2
B.
The triangle is an acute triangle because 5^2<5^2+(√47)^2
C.
The triangle is an acute triangle because (√47)^2<5^2+5^2
D.
The triangle is a right triangle because it has two sides of equal length.
I don't understand but plz help by showing me step by step im so sorry ;-;
Consider the following properties of a triangle
1. If a triangle has an obtuse angle, that angle must be opposite the largest side
2. A triangle can have at most one obtuse angle
3. If a triangle has sides a, b, and c, with c as the largest side,
then if
-- c^2 > a^2 + b^2 , you have an obtuse angle
-- c^2 < a^2 + b^2 , all angles are acute
-- c^2 = a^2 + b^2 , you have a right angled triangle
So.....
since √47 is the larger
which condition fits?
e.g. :
is (√47)^2 > 5^2 + 5^2 ????
or , is 47 > 50 ??
Just noticed that Steve did this for you yesterday. What part of his solution did you not understand, since he did the same thing I just did.
http://www.jiskha.com/display.cgi?id=1464747815
No problem! I'd be happy to help you step by step.
To determine which of the given statements is true, we need to analyze the triangle and check its properties.
First, let's recall the properties of different types of triangles:
1. An obtuse triangle has one angle greater than 90 degrees.
2. An acute triangle has all angles less than 90 degrees.
3. A right triangle has one angle equal to 90 degrees.
Now, let's examine the given triangle:
It has sides of lengths 5 cm, 5 cm, and square root 47 cm.
To determine whether the triangle is obtuse, acute, or right, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let's calculate:
5^2 + 5^2 = 25 + 25 = 50
So, if the triangle is a right triangle, the length of the hypotenuse should be the square root of 50.
Now, let's calculate the square of the given length (√47)^2:
(√47)^2 = 47
Comparing the two values, we see that 47 is not equal to 50. Therefore, the triangle is not a right triangle.
Now, let's compare the values to see if the triangle is obtuse or acute:
(√47)^2 = 47
5^2 + 5^2 = 50
Comparing these values, we see that 47 is less than 50. This implies that the triangle is an acute triangle.
So, the correct statement is:
C. The triangle is an acute triangle because (√47)^2 < 5^2 + 5^2.
I hope this explanation helps! Let me know if you have any further questions.