The perimeter of an isosceles obtuse triangle is 45 cm, and one of its sides is 9 cm larger

| April 5, 2021 | education

The perimeter of an isosceles obtuse triangle is 45 cm, and one of its sides is 9 cm larger than the other. Find the sides of the triangle.

Since the triangle given by the condition is obtuse, at its apex there is an obtuse angle, and at the bases there are acute angles. An obtuse angle is greater than an acute one, so it is fair to assume that the base is larger than the side (the larger the angle, the larger the side on which it rests). Let b be the side and a the base. Since one of the sides of an isosceles triangle is 9 cm larger than the other, then the base is 9 cm larger than the lateral side, then a = b + 9.
The perimeter is:
P = a + 2b;
b + 9 + 2b = 45;
3b = 45 – 9;
3b = 36;
b = 36/3;
b = 12 cm.
Lateral side – b = 12 cm, then the base a = b + 9 = 12 + 9 = 21 (cm).
Answer: the sides are 12 cm each, the base is 21 cm.



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