The perimeter of a triangle is 17 inches. The first side is twice the second. The third side is 3 inches less than the second side. Find the measure of the longest side.

Given:

Perimeter of a triangle = 17 inches

First side is twice the second.

Third side is 3 inches less than the second side.

To find:

The measure of the longest side.

Solution:

Let the second side be x. Then,

First side = 2x

Third side = x-3

We know that, perimeter of a triangle is the sum of all three sides of it.

Divide both sides by 4.

Now,

First side = inches

Second side = 5 inches

Third side =  inches

Therefore, the measure of the longest side is 10 inches.

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).