Answer:
<u>17. BC is 13 √ 2 or 18.38 units. </u>
<u>18. x = 7.</u>
Step-by-step explanation:
1. Let's solve the question 17.
If AC = 26, find BC.
AC is the hypotenuse of the Δ ABC and let's recall that the sides of an square are equal, thus BC = AB = CD = AD
For finding BC , we will use Pythagorean theorem:
Hypotenuse ² = Side ₁ ² + Side₂ ²
Length of Side = x
26 ² = x ² + x ² (BC = AB in a square)
676 = 2x²
338 = x² (Dividing by 2)
x = √ 169 * 2
x = 13 √ 2
BC = 13 √ 2 = 18.38
<u>BC is 13 √ 2 or 18.38 units. </u>
2. Let's solve question 18.
If ∠ ACB = (11x - 32) °, find the value of x.
Recall that a square has four right angles (90 °), thus:
∠ BCD = 90°
But in this case, we're asked to find ∠ ACB , that is formed by the line AC that intersects C in two equal angles : ∠ ACB and ∠ ACD, thus:
∠ ACB and ∠ ACD = 45°
Then, let's find the value of x:
11x - 32 = 45
11x = 45 + 32 (Adding 32 to both sides)
11x = 77
x = 77/11 (Dividing by 11 at both sides)
<u>x = 7</u>
