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Right-angled Triangles, SM-Bank 053

  1. Use Pythagoras' Theorem to calculate the length of the hypotenuse in the isosceles triangle below. Give your answer correct in exact surd form.  (2 marks)
     
           

  2. Using your result from part (a) above, calculate the perimeter of the shape below, correct to 1 decimal place.  (2 marks)
     
         

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a.    \(\sqrt{50}\ \text{cm (exact surd form)}\)

b.    \(30.6\ \text{cm (1 d.p.)}\)

Show Worked Solution

a.    \(\text{Pythagoras’ Theorem states:  }c^2=a^2+b^2\)

\(\text{Let }a=5\ \text{and }b=5\)

\(\text{Then}\ \ c^2\) \(=5^2+5^2\)
\(c^2\) \(=50\)
\(c\) \(=\sqrt{50}\ \text{cm (exact surd form)}\)

 

b.    \(\text{Perimeter}\) \(=\text{chord (a)}\ +\dfrac{3}{4}\times\text{circumference}\)
    \(=\sqrt{50}+\dfrac{3}{4}\times 2\pi r\)
    \(=\sqrt{50}+\dfrac{3}{4}\times 2\pi\times 5\)
    \(=30.633\dots\)
    \(\approx 30.6\ \text{cm (1 d.p.)}\)