Question

You are making a banner in the shape of an isosceles triangle. The banner will have ribbon on the edge. You have 15 yards of ribbon. You want the legs of the banner to each be 5 feet shorter than twice the base. Remember that isosceles triangles have two legs of equal length. What is the length of the base and each leg?

Answer 1

The length and base are 10/3 and 25/3 respectively

Explanation:

Given:

Represent the sides with S and the base with B

Shape: Isosceles Triangle

`S= B- 5`

`Perimeter , P= 15`

Required

Determine the base and legs of the triangle;

The perimeter (P) of a triangle is calculated as thus;

`P = S+ S + B`

`P = 2S + B`

Substitute B- 5 for S

`P = 2(B - 5) + B`

`P = 2B - 10 +B`

Substitute 15 for P

`15 = 2B - 10 + B`

Collect Like terms

`2B + B = 15 + 10`

`3B = 25`

Divide through by 3

`B = (25)/(3)`

Recall that
`S= B- 5`

`S = (25)/(3) - 5`

Take LCM

`S = (25 - 15)/(3)`

`S= (10)/(3)`

Hence, the length and base are 10/3 and 25/3 respectively