Answer:
See below for answers to both questions.
Step-by-step explanation:
Question 13)
We know that the perimeter is the sum of all of the side lengths of the square, and we know that a square has 4 sides that are all the same length. This lets us set up the following equation:
4(10x + 6) = 74
To solve this equation, we should first distribute the 4 through the parentheses using the distributive property.
40x + 24 = 74
Next, we should subtract 24 from both sides of the equation.
40x = 50
Finally, we should divide both sides by 40.
x = 50/40 = 1.25
Therefore, the answer to question 13 is x = 1.25.
Question 14)
If we know the rectangle and triangle have the same perimeter, we can set up the following equation:
2(4x-1) + 2(x-1) = (4x + 1) + (3x + 5) + (x + 1)
We should begin by simplifying the left side of the equation using the distributive property, as we did above.
8x - 2 + 2x -2 = 4x + 1 + 3x + 5 + x + 1
Next, we can combine like terms on both sides of the equation. This means adding together the constant terms (numbers) and also combining the variable terms (x's). This is modeled below:
(8x + 2x) + (-2 + -2) = (4x + 3x + x) + (1 + 5 + 1)
10x - 4 = 8x + 7
Next, we should subtract 8x from both sides.
10x - 8x - 4 = 8x - 8x + 7
2x - 4 = 7
Next, we should add 4 to both sides.
2x - 4 + 4 = 7 +4
2x = 11
Finally, we should divide both sides by 2.
x = 11/2 = 5.5
The question asks us to find the perimeter, so we can use the perimeter of the rectangle:
10x - 4 = 10(5.5) - 4 = 51
Therefore, the answer is 51 units.
Hope this helps!
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