The unequal side of an isosceles triangle is 5 cm longer than its equal sides. If the perimeter of the triangle is 20 cm, find the length of the unequal side?

Answer 1

In order to answer this problem you will need to know the definition of an isosceles triangle (If you read the problem statement carefully it hints at this definition but please refer to the definition below).

An Isosceles triangle is specified as a triangle with 2 of its 3 sides having equal lengths.

Step 1: Draw your triangle.

1. Since 2 of your 3 sides are equal length, you are dealing with a right triangle or, properly named, a right angled isosceles triangle.

Step 2: Label your triangle sides.

1. Since we do not know the value of the equal sides lengths, we can use a place holder value of 'x'.
2. Since we know that the uneven side is 5 cm longer, we can use a place holder value of '(x+5)'.

Step 3: Write an equation.

1. Use the equation for perimeter (P = a + b  + c) where the following is true:

“equal sides” or a & b = (x)

“unequal side” = c = ( x + 5 )

Step 4: Solve for x.

Equation: P = a + b  + c

Plug in: 20 = (x) + (x)  + ( x + 5 )

Simplify: 20 = 2x + ( x + 5 )

Simplify: 20 = 3x + 5

Subtract: 15 = 3x

Divide: 5 = x

Step 5: Find length of unequal side.

“unequal side” = c = ( x + 5 ) = ( 5 + 5) = 10

“unequal side” = 10 cm