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Answer:
C. 19
Step-by-step explanation:
90+26=116
180-116=64
3x+7=64
3x=57
x=19
we know that
The formula to calculate the slope between two points is equal to
we have
Step 1
<u>Find the slope GH</u>
substitute in the formula
Step 2
<u>Find the slope HJ</u>
substitute in the formula
Step 3
<u>Find the slope JG</u>
substitute in the formula
Step 4
Verify if triangle GHJ is a right triangle
we know that
if two lines are perpendicular, then the product of their slopes is equal to minus one
so
compare slope GH with slope JG
we have
-----> side GH and side JG are perpendicular
The triangle GHJ is a right triangle
The answer in the attached figure
Based on the calculations, the exact area of this rectangle is equal to 16√3 + 32 mm².
<h3>How to calculate the area of a rectangle?</h3>
Mathematically, the area of a rectangle can be calculated by using this formula:
Area = Length × Width
Note: Radius (R) is equal to 2 mm.
Joining the center of the circles would form an equilateral triangle with side length of 2R. Also, the height of the equilateral triangle is given by:
Height = √2R² - R²
Height = √3R
For the length and width of this rectangle, we have:
Length = R + 2R + R
Length = 4R
Width = 2R + height of equilateral triangle
Width = 2R + √3R
Width = (2 + √3)R
Therefore, the area of a rectangle becomes:
Area = 4R × (2 + √3)R
Area = 4(2 + √3) × R²
Area = 4(2 + √3) × 2²
Area = (8 + 4√3) × 4
Area = 16√3 + 32 mm² ≡ a√3 + b
In conclusion, a = 16 and b = 32.
Read more on rectangle here: brainly.com/question/25292087
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Answer:
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