a.
To find: The area of a
a.
Answer to Problem 4PSB
The area of a triangle with sides 2, 5 and 7 is 0.
Explanation of Solution
Given Information:
Sides of the triangle are:
Formula used:
Using Heron’s formula,
Area of a triangle
Here,
Calculation:
Let
We know that, Area of an inscribed quadrilateral
Now,
So,
So, the area of a triangle is 0.
Hence, there is no triangle with the sides 2, 5 and 7.
b.
To calculate: The area of a triangle with sides 4, 6 and 12.
b.
Answer to Problem 4PSB
There does not exist any triangle with sides 4, 6 and 12.
Explanation of Solution
Given Information:
Sides of the triangle are:
Formula used:
Using Heron’s formula,
Area of a triangle
Here,
Calculation:
Let
We know that, Area of an inscribed quadrilateral
Now,
So,
This is not defined as it is a square root of a negative number..
Hence, there is no triangle with the sides 4, 6 and 12.
c.
To explain: the results obtained in parts a and b.
c.
Answer to Problem 4PSB
No such triangles exist.
Explanation of Solution
Given Information:
1st triangle has sides:
2nd triangle has sides:
Formula used:
Sum of any two sides of a triangle is always greater than the third side
1st triangle has sides:
2nd triangle has sides:
In a triangle, sum of any two sides is always greater than the third side.
But
So, the sides
Also,
So, the sides
Hence, no such triangles exist.
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