21. In A ABC, A+B = 18 units, B + C = 25
units an C +A= 17 units. What type of A
is ABC. Give reason.
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In ∆ABC,
AB + BC = 18 => BC = 18 - AB
BC + CA = 25 => CA = 25 - BC = 25 - (18 - AB)
=> CA = 7 + AB
AB + CA = 17
AB + 7 + AB = 17
2AB = 17 - 7
2AB = 10
AB = 5
substituting in BC = 18 - AB, we get
BC = 13
substituting in CA = 7 + AB, we get
CA = 12
now,
AB² + CA² = 12² + 5² = 144 + 25 = 169 = 13² = BC²
hence, ∆ABC is a right angled triangle with BC as hypotenuse and angle A as the right angle.
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