Answer:
The answer to your question is Area = 620 m²
Step-by-step explanation:
Process
Find the area of the different parts of the prism and later added them.
1.- Area of the base
Area of a rectangle = 10 m x 24 m = 240 m²
2.- Area of the lateral sides (there are 2)
Area of a rectangle = 10 x 13 x 2 = 260 m²
3.- Area of the triangles (there are 2)
Calculate the height using the pythagorean theorem
13² = 12² + b²
b² = 13² - 12²
b² = 169 - 144
b² = 25
b = 5
Area = 1/2 (24 x 5) x 2 = 120 m²
4.- Total area
Area = 120 + 260 + 240
= 620 m²
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Answer:
See Explanation
Step-by-step explanation:
Solving (a): The Variables
The variables are the ages of Jaime, Crystal and Marissa;
Let
x represents Jaime's age;
y represents Crystal's age;
z represents Marissa's age
Solving (b): Equation
![x = 3 + y](https://tex.z-dn.net/?f=x%20%3D%203%20%2B%20y)
![z = 2x](https://tex.z-dn.net/?f=z%20%3D%202x)
![x + y + z = 45](https://tex.z-dn.net/?f=x%20%2B%20y%20%2B%20z%20%3D%2045)
Solving (c): Result of the equations
-- (1)
-- (2)
-- (3)
Make y the subject in (1)
![y = x - 3](https://tex.z-dn.net/?f=y%20%3D%20x%20-%203)
Substitute
and
in (3)
![x + y + z = 45](https://tex.z-dn.net/?f=x%20%2B%20y%20%2B%20z%20%3D%2045)
![x + x - 3 + 2x = 45](https://tex.z-dn.net/?f=x%20%2B%20x%20-%203%20%2B%202x%20%3D%2045)
Collect Like Terms
![x + x + 2x = 45 + 3](https://tex.z-dn.net/?f=x%20%2B%20x%20%2B%202x%20%3D%2045%20%2B%203)
![4x= 48](https://tex.z-dn.net/?f=4x%3D%2048)
Solve for x
![x = 48/4](https://tex.z-dn.net/?f=x%20%3D%2048%2F4)
![x = 12](https://tex.z-dn.net/?f=x%20%3D%2012)
Substitute
in
and ![z = 2x](https://tex.z-dn.net/?f=z%20%3D%202x)
![y= 12 - 3](https://tex.z-dn.net/?f=y%3D%2012%20-%203)
![y = 9](https://tex.z-dn.net/?f=y%20%3D%209)
![z = 2x](https://tex.z-dn.net/?f=z%20%3D%202x)
![z = 2 * 12](https://tex.z-dn.net/?f=z%20%3D%202%20%2A%2012)
![z = 24](https://tex.z-dn.net/?f=z%20%3D%2024)
This implies that;
Jaime is 12; Crystal is 9 and Marissa is 24 years old
Solving (d): Essence of the question
The question asks that we solve for the ages of Jaime, Crystal and Marissa
1. Input:1, output:4
2. Input:1, output:6
3. Input:5, output:8
3. Input:5, output:10
The different between the inputs and outputs are 3, 5, 3, 5. See the pattern?
Hope this helped.