In an isosceles trapezoid, the lower base is 15, the upper base is 5, and each leg is 6. How far must each of the legs be extended to form a triangle?

Answer:

3 units

Explanation:

Let the side of the triangles to be extended be x. Both sides of the triangle are equal.

Applying similarly theorem of two similar triangles, the following proportion can be set up to solve for the value of x as shown below:

[tex] \frac{15}{5} = \frac{6 + x}{x} [/tex]

Cross multiply

[tex] 15 \times x = (6 + x) \times 5 [/tex]

[tex] 15x = 30 + 5x [/tex]

Subtract both sides by 5x

[tex] 15x - 5x = 30 [/tex]

[tex] 10x = 30 [/tex]

Divide both sides by 10

[tex] x = 3 [/tex]

Therefore, the legs must be extended 3 units more to form a triangle.

Each of the legs be extended by 3 to form a triangle

Using the theorem of two similar triangles, Assuming that sides of the triangle are equal, we can extend the side of the triangles with [tex]y[/tex]

We can create a proportion as;

[tex]\frac{ y }{ 6+y } = \frac{5}{15}[/tex]

Cross multiply, we have

[tex]30 =15y-5y[/tex]

[tex]30=10y[/tex]

[tex]y= \frac{30}{10}[/tex]

[tex]y=3[/tex]

Therefore, each of the legs be extended by 3 to form a triangle

Learn more about isosceles trapezoid at:

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