An isosceles triangle has two sides of equal length. The length of the third side is 1 m less than twice the length of one of the equal sides. Find the length

Question

translate the problem from words to mathematical expressions and then solve.

Answer 1

Since the legs of the triangle are equal in length, it could be a 45-45-90 triangle.  This means that one of the angles of the triangle is 90 degrees, indicating a right triangle, since isosceles triangles also have two equal angles due to fact that they have equal side lengths.

 

Let one leg = x

Let the other leg = x

Third leg = 2x - 1

 

Let's use Pythagorean theorem.

 

x² + x² = (2x - 1)²

2x² = 4x² - 4x + 1

 

Subtract x² on both sides of equation. 

 

0 = 2x² - 4x + 1

 

 

Use the quadratic formula to solve for x, since we cannot factor using FOIL.

 

x = (4 ± √(16 - 4(2))) / 4

 

x = (4 ± √(8)) / 4

 

x = (4 ± 2.83) / 4

 

x = 1.71        and         x = 0.29

 

We accept the x = 1.71 because x = 0.29 will result in a near zero dimension for the sides.

 

 

The length is 1.71m