The area of the triangle PQR is 108 square units
<h3>How to determine the area of the triangle?</h3>
The given parameters are:
- Height, h = 12 units
- Base, b = 18 units
The area is then calculated using:
Area = 0.5 * base * height
So, we have:
Area = 0.5 * 18 * 12
Evaluate
Area = 108
Hence, the area of the triangle PQR is 108 square units
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Answer:
Case 1:
Case 2:
Case 3: Not possible
Step-by-step explanation:
Given
See attachment for illustration of each case
Required
Find AB and BC
Case 1:
Using Pythagoras theorem in ANB, we have:
This gives:
Take square roots of both sides
To calculate BC, we consider ANC, where:
Collect like terms
Take square roots
So:
Case 2:
Using Pythagoras theorem in ANB, we have:
This gives:
Collect like terms
Take square roots of both sides
To calculate BC, we consider ABC, where:
Collect like terms
Take square roots
Case 3:
This is not possible because in ANC
The hypotenuse AN (24) is less than AC (40)
Answer:
(2, 1)
Step-by-step explanation:
The best way to do this to avoid tedious fractions is to use the addition method (sometimes called the elimination method). We will work to eliminate one of the variables. Since the y values are smaller, let's work to get rid of those. That means we have to have a positive and a negative of the same number so they cancel each other out. We have a 2y and a 3y. The LCM of those numbers is 6, so we will multiply the first equation by a 3 and the second one by a 2. BUT they have to cancel out, so one of those multipliers will have to be negative. I made the 2 negative. Multiplying in the 3 and the -2:
3(-9x + 2y = -16)--> -27x + 6y = -48
-2(19x + 3y = 41)--> -38x - 6y = -82
Now you can see that the 6y and the -6y cancel each other out, leaving us to do the addition of what's left:
-65x = -130 so
x = 2
Now we will go back to either one of the original equations and sub in a 2 for x to solve for y:
19(2) + 3y = 41 so
38 + 3y = 41 and
3y = 3. Therefore,
y = 1
The solution set then is (2, 1)
Answer:
x = 3
Step-by-step explanation:
6x + 2x - 5= 19
8X -5 = 19
8x = 24
x = 3
Answer:
13
Step-by-step explanation:
The top must be the same length as the total of the bottom
top = 5+8
top = 13
