What is the perimeter of this rug?

Question

The factory makes a triangular rug. It is an isosceles triangle 4 feet wide with a perpendicular height of 1 foot 6 inches. How much braid will Hank need to cut to go all around this rug? Thank You!

Answer 1

Hi Paula, the perimeter of the triangle is the sum of the sides. In an isosceles triangle, two sides are equal in length.

 

An equation for the perimeter of an isosceles triangle would be: P = 2 * S₁ + B, where P is the perimeter, S₁ is the length of one of the isosceles legs, and B is the base.

 

Let the triangle be represented by XYZ with Y being the apex or top of the triangle. Sides XY and ZY are the two isosceles sides and the base would be XZ. If we drop a line straight down from the apex or top of the triangle to the base, the line will be perpendicular to the base and will cut the base into two equal parts of 2 feet in length.

 

To solve the problem, we can use the Pythagorean Theorem on one of the two triangles formed, c² = a² + b², where c is the hypotenuse and one of the two isosceles legs we need to find the length of, a is the height (1 foot 6 inches), and b is the base (1/2 of 4 feet).

 

Substituting for the height and base gives:

 

Note: 1 foot 6 inches = 1.5 feet.

 

c² = 1.5² + 2²

 

c² = 2.25 + 4

 

c² = 6.25

 

c = √6.25 = 2.5

 

The perimeter of the isosceles triangle is:

 

P = 2 * 2.5 + 4 = 9 feet.

 

Hank will have to cut 9 feet of braid to go all around the rug.