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.
My answer for this Q is A :D
so, you're saying that 47 > 50 ?
ok so now check your answer by doing it the other way
and see if u get the same answer
To determine which statement is true, we need to first calculate the squares of each side.
The first statement, A, states that the triangle is an obtuse triangle because (√47)^2 > 5^2 + 5^2.
Calculating the squares:
(√47)^2 = 47
5^2 = 25
5^2 = 25
Therefore, the inequality becomes 47 > 25 + 25, which simplifies to 47 > 50. However, this statement is incorrect because 47 is not greater than 50.
Now let's move on to the second statement, B, which states that the triangle is an acute triangle because 5^2 < 5^2 + (√47)^2.
Calculating the squares:
5^2 = 25
5^2 = 25
(√47)^2 = 47
The inequality becomes 25 < 25 + 47, which simplifies to 25 < 72. This statement is also incorrect because 25 is indeed less than 72.
Next, let's evaluate the third statement, C, which states that the triangle is an acute triangle because (√47)^2 < 5^2 + 5^2.
Calculating the squares:
(√47)^2 = 47
5^2 = 25
5^2 = 25
The inequality becomes 47 < 25 + 25, which simplifies to 47 < 50. This statement is incorrect as well because 47 is not less than 50.
Finally, let's analyze the fourth statement, D, which states that the triangle is a right triangle because it has two sides of equal length.
Since the triangle has two sides of length 5 cm, this means it is an isosceles triangle. However, having two sides of equal length does not necessarily imply that it is a right triangle. Therefore, statement D is also incorrect.
So, none of the given statements is true for this particular triangle.