On a square gameboard that is divided into n rows of n squares each, k of these squares do not lie along the boundary of the gam
eboard. If k is one of the four numbers 10, 25, 34, or 52, what is a possible value for n?
1 answer:
Answer: 7
Step-by-step explanation:
-if y is the width and the length of area k (see diagram), the difference between n and y is of 2 square sides, one at each side of y.
-therefore, assuming that n is a whole number and that there aren’t half squares, y must be a whole number too because, as previously said, n-y = 2 so y= n -2
-the only perfect square amongst the values for k you listed is 25, so taking n and y as whole numbers the only possible value for k is 25
-therefore y is 5 and n is 7 because n-y = 2 so y + 2 = n
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Answer:
The proof is derived from the summarily following equations;
∠FBE + ∠EBD = ∠CBA + ∠CBD
∠FBE + ∠EBD = ∠FBD
∠CBA + ∠CBD = ∠ABD
Therefore;
∠ABD ≅ ∠FBD
Step-by-step explanation:
The two column proof is given as follows;
Statement Reason
bisects ∠CBE
Given
Therefore;
∠EBD ≅ ∠CBD Definition of angle bisector
∠FBE ≅ ∠CBA Vertically opposite angles are congruent
Therefore, we have;
∠FBE + ∠EBD = ∠CBA + ∠CBD Transitive property
∠FBE + ∠EBD = ∠FBD Angle addition postulate
∠CBA + ∠CBD = ∠ABD Angle addition postulate
Therefore;
∠ABD ≅ ∠FBD Transitive property.