Question

A company makes traffic signs one of those signs can be modeled by an equilateral triangle with the perimeter of 144 inches the company makes the summer sun with a perimeter that is 1.25 times the one above what is the height in inches of the larger

Answer 1

The height of the larger traffic signs is 51.96 inches

Explanation:

Given that initially, A company makes traffic signs of an equilateral triangle with the perimeter of 144 inches

Now, A company makes similar traffic signs of perimeter 1.25 of original

New perimeter will be 1.25x144=180 inches

Let triangle ABC be a larger triangle with 180inches of the perimeter.

It is given that the triangle is an equilateral triangle,

Therefore, Side AB=BC=AC

The perimeter of a triangle ABC is

AB+BC+AC=180

3AB=180

AB=60 inches

Figure show that triangle ABC and AD is the height of the triangle.

Since, the triangle ABC is an equilateral triangle,

AD is the perpendicular bisector of BC

so that,

BD=DC and Angle ADB=90

In right triangle ADB,

Angle D =90 and Angle B =60

Side BD=60/2=30 inches and AB=60 inches

Using Pythagoras theorem,

`AD^(2) +BD^(2) =AC^(2)`

`(AD)^(2) +(30)^(2) =60^(2)`

`(AD)^(2) =60^(2)-(30)^(2)`

AD=51.96 inches

Thus, The height of the larger traffic signs is 51.96 inches