I don’t understand this. We haven’t been taught it and I don’t wanna fail my exam.

Question

A triangle has vertices at points (0,7), (6,7), and (3,0). What’s the perimeter?

Answer 1

One leg of the triangle runs from (0,7) to (6,7), so its length is easy: 6.

For the other two, we have to work a bit more. If you imagine a line segment from (3,0) to (3,7), that will form 2 congruent right triangles with sides of 3 and 7. The two unknown sides of the original triangle are the hypotenuses of these smaller triangles, so we can find its length using the Pythagorean Theorem:

x² = 3² + 7² = 9 + 49 = 58, so x ≅ 7.6, making the perimeter approximately 21.2

Answer 2

Hello Sky,

First, take a deep breath counting up to 3 or 4 for the inhale and then counting again during the exhale and don't panic about your test!

Now, depending on what you have covered in your class, your teacher will be expecting you to use either the pythagorean theorem OR the distance formula to solve for the perimeter.

Plotting the points is very effective whenever you need a visual to help identify the sides or angles of a regular polygon. You'll see the (6,7) coordinate reveals the base of the triangle (which is 6 units in length). The height is 7 units (recognized by the (0,7) and (6,7) coordinate points.

Using the Pythagorean theorem: a² + b² = c² to find the hypotenuse.

3² + 7² = c² thus, 9 + 49 = c²

58 = c² then taking the square root (sqrt) of each side, we get the following:

sqrt(58) = sqrt(c²) when simplified gives us the sqrt(58) = c

Now, multiply the hypotenuse [sqrt(58)] by 2 (since there are 2 sides of equal length here that must be included as part of the perimeter).

Take the 2*sqrt(58) and add the 6 units from the base of the triangle to give you 21.23 units.

Using the distance formula: sqrt[(x₂-x₁)²+ (y₂-y₁)²]

Choose any two appropriate ordered pairs to calculate this. I am using (0,7) and (3,0) but you can also choose (3,0) and (6,7).

Plug in your numbers to give you: sqrt[(3-0)²+ (0-7)²]

Simplify the equation to get: sqrt[(3)²+ (-7)²] = sqrt(9+49) = sqrt(58)

Again, this is the hypotenuse (of which you have two).

So, sqrt(58) x 2 = 2*sqrt(58)

Add in the 6 from the base to get: 6 + 2*sqrt(58) which is approximately 21.23 units for the perimeter!!

Please send me a message if you have additional questions regarding this problem or other concepts that will be on your exam tomorrow!. I'm always happy to help :)

Jasmine