Answer: 
Step-by-step explanation:
1. You have the following formula for calculate the area of the original circular chip:

Where D is the diameter of the circle.
2. Then, if the diameter of the original circular chip is doubled (2D) to use in a new board game, the area of the new chip can be calculated with the following formula:

The first thing you want to do is isolate the (x)s.
Given the parameters in the diagrams, we have;
4. ∆ABC ≈ ∆DEF by ASA
5. UW ≈ XZ by CPCTC
6. QR ≈ TR by CPCTC
<h3>How can the relationship between the triangles be proven?</h3>
4. The given parameters are;
<B = <E = 90°
AB = DE Definition of congruency
<A = <D Definition of congruency
Therefore;
- ∆ABC ≈ ∆DEF by Angle-Side-Angle, ASA, congruency postulate
5. Given;
XY is perpendicular to WZ
UV is perpendicular to WZ
VW = YZ
<Z = <W
Therefore;
∆UVW ≈ ∆XYZ by Angle-Side-Angle, ASA, congruency postulate
Which gives;
- UW is congruent to XZ, UW ≈ XZ, by Corresponding Parts of Congruent Triangles are Congruent, CPCTC
6. Given;
PQ is perpendicular to QT
ST is perpendicular to QT
PQ ≈ ST
From the diagram, we have;
<SRR ≈ <PRQ by vertical angles theorem;
Therefore;
∆QRP ≈ ∆TRS by Side-Angle-Angle, SAA, congruency postulate
Which gives;
- QR ≈ TR by Corresponding Parts of Congruent Triangles are Congruent, CPCTC
Learn more about congruency postulates here:
brainly.com/question/26080113
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<u>We are given the expression:</u>
√-3 * √-27
__________________________________________________________
<u>Explaining the concept:</u>
We know that:
√ab = √a * √b
Using this concept, we will simplify the given expression and solve it
__________________________________________________________
<u>Simplifying the expression:</u>
√-3 * √-27
√(-1*3) * √[(-1)*(3)(3)(3)]
√-1 * √3 * √-1 * √3 * √3 * √3
(√-1 * √-1) * (√3 * √3 * √3 * √3)
(√-1)² * (√3)² * (√3)²
-1 * 3 * 3
-9
Hence, after simplifying the given expression, we get -9