Question 596285: An isosceles triangle has a base length of 6m and a perimeter of 22m. Write an equation and solve it to find the length of the equal sides. Please show work I do not understand this problem.
Answer by math-vortex(648)   (Show Source):
You can put this solution on YOUR website! Hi, there!
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We want to find the unknown side lengths of this triangle. To solve this problem, we need to use some definitions. Definitions are very important in mathematics.
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An ISOSCELES triangle is a triangle that has two sides with equal length.
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The PERIMETER of the triangle is the distance around the three sides of the triangle.
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The BASE of the triangle can be any one of the three sides. Usually, it's the one drawn on the bottom.
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I will solve this problem in words first. Then I'll show you how to write and solve an equation.
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OK. We know that the base of the triangle is 6 meters (6m). We also know that the perimeter is 22 meters (22m). The difference between 22 and 6 is 22-6=16. So we have 16m left to divide between the other two sides.
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Because this is an isosceles triangle, we know that the other two sides have the same length. We ask, "What number times two equals 16?" The answer is 8 because 16 divided by 2 is 8.
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So the lengths of the two equal sides are 8 meters (8m).
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To write an equation, we need a variable for the unknown side lengths. I'll use x, but you can use any variable you like.
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We use the fact that the three sides add up to the perimeter, 22m. So the equation in words is
[perimeter] = [base length] + [side length] + [side length]
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In algebra, we write the equation as
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To solve the equation, we combine like terms first: x + x = 2x
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Subtract 6 from both sides of the equation to get the 2x by itself.
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2 times x is 16. We want to know what x is, so we divide both sides by 2.
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By algebra, we see that the length of the equal sides are 8m.
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Please email me, if you still have a question about this.
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Good luck!
Ms.Figgy
math.in.the.vortex@gmail.com
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