How do I find the perimeter of a right triangle with Base: 2x+6, Height: x+2, and Hypotenuse: x+10?

Question

I tried setting up an equation for perimeter and area. But I couldn't figure out how to substitute the values.

Answer 1

Since the base we're using is not the hypotenuse, we can use the fact that it's a right triangle to conclude that the non-base leg of the triangle is actually the height. Thus the base, height, and hypotenuse must form a pythagorean triple.

(2x+6)^2 + (x+2)^2 = (x+10)^2
4x^2 + 24x + 36 + x^2 + 4x + 4 = x^2 + 20x + 100
5x^2 + 28x + 40 = x^2 + 20x + 100
4x^2 + 8x - 60 = 0
4(x^2 + 2x - 15) = 0
4(x +5)(x-3) = 0
x = -5 or x = 3

We can't have x=-5 since that makes the height negative, so for the perimeter we use x=3 to calculate P = 2(3) + 6 + (3) + 2 + (3) + 10 = 30.

For area, we use A = (1/2)*(12)(5) = 30.

Answer 2

to find the peimeter and area, you first need to find the sides

you use pythagarean theorem
a^2 + b^2 = c^2

a and b are the legs
c is the hypotenue


(2x + 6)^2 + (x+2)^2 = (x + 10)^2

4x^2 + 24x + 36 + x^2 + 4x + 4 = x^2 + 20x + 100

5x^2 + 28x + 40 = x^2 + 20x + 100

4x^2 + 8x - 60 = 0

factor

4 (x^2 + 2x - 15) = 0

4 (x + 5) (x - 3) = 0

x = -5 or 3

since distance can't be negative, 3 is the answer

plug 3 back in for x to find the sides

base = 2(3) + 6 = 12
height = 3 + 2 = 5
hypot: 3 + 10 = 13


Perimeter = 12 + 5 + 13 = 30

Area = 1/2 base * height
Area = 1/2 (12) (5)
Area = 30

hope this helps

Answer 3

Add those three lengths up. As the triangle is right-angled, the height is the third side. The perimeter is the sum of the lengths of the sides. There is no need to find the area.
The perimeter is:
2x + 6 + x + 2 + x + 10
= 4x + 18.

Answer 4

(x+10)^2 = (2x+6)^2 + (x+2)^2
x^2+20x +100 = 4x^2 +24x +36 +x^2 +4x +4
- 4x^2 -8x +60 = 0
x^2 +2x -15 = 0
(x+5)(x-3) = 0
x= 3 (x=-5 is rejected because it would result in -ive side
So perimeter = x+10+ x+2+ 2x+6
= 3+10 +3 + 2 + 3*2+6 = 30
This is a 5-12-13 rt triangle.

Answer 5

The perimeter is the sum of the lengths of the 3 sides so
P = (2x+6) + (x+2) + (x+10) = 4x +18

Answer 6

For perimeter all you do is add all of the sides together.. so you have:
2x+6 + x+2 + x+10... now add
4x+18.
That is your answer.

If you need area, the formula is 1/2(length of the base) times the height..
that would be..
{(2x+6)/2} * (x + 2)=
(x+3)(x+2)= x^2 + 5x + 6.

P = 4x+18.
A = x^2+5x+6.

Answer 7

The perimeter is simply the sum of the sides of a certain 2-dimensional figure. (In this case, a triangle).

so, given the 3 sides; add them up.

(2x + 6) + (x + 2) + (x+10) = 4x + 18

4x+ 18 = perimeter

best answer please :P

Answer 8

use Pythagoras: (2x+6)^2+(x+2)^2 = (X+10)^2
<=> 4x^2+24x+36+x^2+4x+4 = x^2+20x+100
<=>4x^2+8x-60 = 0
<=>x^2+2x-15=0
<=>x(x+2)=15
===>x=3

Answer 9

Add the three lengths given.

Perimeter = 4x + 18.