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Perhatikan gambar.
Jika panjang 
AD=16cm dan 
AB=25cm, Panjang 
BC adalah ....
A. 
12cm
B. 
15cm
C. 
16cm
D. 
20cm

99. Perhatikan gambar.\newlineJika panjang AD=16 cm A D=16 \mathrm{~cm} dan AB=25 cm A B=25 \mathrm{~cm} , Panjang BC \mathrm{BC} adalah ....\newlineA. 12 cm 12 \mathrm{~cm} \newlineB. 15 cm 15 \mathrm{~cm} \newlineC. 16 cm 16 \mathrm{~cm} \newlineD. 20 cm 20 \mathrm{~cm}

Full solution

Q. 99. Perhatikan gambar.\newlineJika panjang AD=16 cm A D=16 \mathrm{~cm} dan AB=25 cm A B=25 \mathrm{~cm} , Panjang BC \mathrm{BC} adalah ....\newlineA. 12 cm 12 \mathrm{~cm} \newlineB. 15 cm 15 \mathrm{~cm} \newlineC. 16 cm 16 \mathrm{~cm} \newlineD. 20 cm 20 \mathrm{~cm}
  1. Identify Right-Angled Triangle: We know triangle ABCABC is right-angled at BB, so we can use Pythagoras' theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
  2. Calculate Length of BC: Let's calculate the length of BC using the Pythagorean theorem: AB2=BC2+AD2AB^2 = BC^2 + AD^2.
  3. Substitute Given Lengths: Substitute the given lengths into the equation: 252=BC2+16225^2 = BC^2 + 16^2.
  4. Calculate Squares: Calculate the squares: 625=BC2+256625 = BC^2 + 256.
  5. Isolate BC2BC^2: Subtract 256256 from both sides to isolate BC2BC^2: BC2=625256BC^2 = 625 - 256.
  6. Find Square Root: Calculate the difference: BC2=369BC^2 = 369.
  7. Calculate BC: Find the square root of BC2BC^2 to get BC: BC=369BC = \sqrt{369}.
  8. Calculate BC: Find the square root of BC2BC^2 to get BCBC: BC=369BC = \sqrt{369}.Calculate the square root: BC=19.2BC = 19.2, but this is not one of the options, so we must have made a mistake.