Eight isosceles right-angled triangles, whose sides coincide as shown, form a shape whose perimeter is an irregular nonagon. The shortest side of the nonagon has length 1cm . Calculate the perimeter of the nonagon, giving your answer in the form (a)b +(square root))cm .
The easiest approach to this question is to label each side with a length. It is important to notice that, because every triangle is similar, the ratios of their sides are the same for every triangle – so the hypotenuse is always (square root equation) times the length of the shorter sides.
Now all that’s left to do is add all the lengths up, adding the integers and surds separately.
1 + 2 + 4 + 8 + 15 = 30
(square root equation)
(square root equation)