3. A kitchen garden is triangular in shape with sides 6m, 8m, 10m. Its owner wants to divide her
field into four congruent triangles to grow four different types of flowers on them. Find the:
i) maximum dimensions of the congruent triangles in which the field can be divided
ii) area of each triangle

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Solution

$D e a r S t u d e n t G i v e S i d e s o f t r i a n g l e a s 6 m, 8 m, 10 m A r e a o f t r i a n g u l a r g a r d e n = \sqrt{s (s - a) (s - b) (s - c)}, s = \frac{a + b + c}{2} s = \frac{6 + 8 + 10}{2} = 12 n o w a r e a = \sqrt{12 (12 - 6) (12 - 8) (12 - 10)} = \sqrt{12 \times 6 \times 4 \times 2} = \sqrt{576} = 24 c m^{2} G i v e n o w n e r w a n t s t o d i v i d e t h e t r i a n g l e i n t o 4 c o n g r u e n t t r i a n g l e s . t h e m a x i m u m d i m e n s i o n i s p o s s i b l e w h e n t h e t r i a n g l e i s d i v i d e d i n t o e q u i l a t e r a l t r i a n g l e . t h e r e f o r e a r e a o f o n e e q u i l a t e r a l t r i a n g l e = \frac{24}{4} = 6 c m^{2} d i m e n s i o n o f e q u i l a t e r a l t r i a n g l e = a a r e a o f t r i a n g l e = \frac{\sqrt{3}}{4} a^{2} 6 = \frac{\sqrt{3}}{4} a^{2} 24 = \sqrt{3} a^{2} \frac{24}{\sqrt{3}} = a^{2} a = \sqrt{13.85} c m R e g a r d s$

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