Answer:
3 < c < 13
Step-by-step explanation:
A triangle is known to have 3 sides: Side a, Side b and Side c.
For a triangle, one of the three sides is longer than the other two sides. (The only exception is when we are told specifically that a triangle is an equilateral triangle, where all the 3 sides are equal to each other).
To solve the above question, we would be using the Triangle Inequality Theorem.
The Triangle Inequality Theorem states that the summation or addition of the lengths of any two sides of a triangle is greater than the length of the third side.
Side a + Side b > Side c
Side a + Side c > Side b
Side b + Side c > Side a
For the above question, we have 2 possible side lengths for the third side of the triangle. We are given in the above question,
side (a) = 5
side (b) = 8
Let's represent the third side as c
To solve for the above question,we would be having the following Inequality.
= b - a < c < b + a
= 8 - 5 < c < 8 + 5
= 3 < c < 13
Answer:
B) 3/2
Step-by-step explanation:
Answer:
D₁ = 68°
Step-by-step explanation:
If AB = BE then ΔABE is an isosceles triangle, therefore A₁ = E₁.
If A₁ = 28° then E₁ = 28°.
<u>Opposite sides</u> of a parallelogram are <u>parallel</u>.
Using the Alternate Interior Angles Theorem:
A₂ = E₁ = 28°
Therefore, A = A₁ + A₂ = 28° + 28° = 56°
<u>Opposite angles</u> in a parallelogram are <u>equal</u>.
Therefore, C = A = 56°.
<u>Opposite sides</u> of a parallelogram are <u>equal in length</u>, so AB = CD.
If AB = DE = CD then ΔCDE is an isosceles triangle.
Therefore, C = E₃ = 56°.
Interior angles of a triangle sum to 180°.
⇒ D₁ + C + E₃ = 180°
⇒ D₁ + 56° + 56° = 180°
⇒ D₁ + 112° = 180°
⇒ D₁ = 180° - 112°
⇒ D₁ = 68°
Answer:
3.2
Step-by-step explanation:
The two numbers are 120 and 60
Let's call the two numbers x and y. The first sentence translates into

from which we can derive

So, their product can be written as

This expression is a quadratic polynomial with negative leading coefficient, so it represents a parabola concave down. So, the vertex of the parabola is its maximum, which we can find as usual: given the parabola
, its extreme point is located at
.
So, in your case, since
and
, the maximum is located at

Now that we know y, we can deduce the value of x:

So, the two numbers are 120 and 60