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A day full of math games & activities. Find one near you.
The lengths of the sides of a triangle are 3x, 5x - 12, and x + 20. Find the value of x so that the triangle is isosceles?
Solution:
An isosceles triangle is one in which the two sides of a triangle are equal in length.
The three sides given are 3x, 5x - 12 and x + 20.
The three possibilities are:
(1) 3x = 5x - 12
(2) 3x = x + 20
Or
(3) 5x - 12 = x + 20
From (1) we have
3x = 5x - 12
12 = 5x - 3x
12 = 2x
x = 6
The sides are then 18, 18 and 26
From (2) we have
3x = x + 20
2x = 20
x = 10
The three sides are then 30, 38 and 30
From (3) we have
5x - 12 = x + 20
4x = 32
x = 8
The three sides are then 24, 28, 28
The lengths of the sides of a triangle are 3x, 5x - 12, and x + 20. Find the value of x so that the triangle is isosceles?
Summary:
The lengths of the sides of a triangle are 3x, 5x - 12, and x + 20. The value of x so that the triangle is isosceles is 8, 6 or 10
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