Answer:
x = 28 cm
Step-by-step explanation:
Given:
Area of link shaded regions = 84 cm²
Required:
The value of x (diameter of the semicircle/length of the rectangle)
Solution:
Diameter of the semicircle = 2r = x
Length of rectangle (L) = 2r = x
Radius of semicircle (r) = ½x
Width of rectangle (W) = radius of semicircle = ½x
Use 3.14 as π
Area of the link shaded regions = area of rectangle - area of semicircle
Thus:
Area of the link shaded regions = (L*W) - (½*πr²)
Plug in the values
84 = (x*½x) - (½*3.14*(½x)²)
84 = x²/2 - (1.57*x²/4)
84 = x²(½ - 1.57/4)
84 = x²(0.5 - 0.3925)
84 = x²(0.1075)
Divide both sides by 0.1075
84/0.1075 = x²
781.4 = x²
√781.4 = x
27.9535329 = x
x = 28 cm
Answer:
15 cm²
Step-by-step explanation:
5 + 1 + 1 = 7
7 × 5 = 35
5 × 1 = 5
5 + 5 + 5 + 5 = 20
35 - 20 = 15
This can be written as (x+4)(x+4)
Multiply everything in the second parenthesis by the x.
x^2 + 4x
Multiply everything in the second parenthesis by 4.
4x + 16
Add these two equations together.
x^2 + 4x + 4x + 16
Combine like terms.
x^2 + 8x + 16
Hope this helps!
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