Question

(c) The measures of the sides of a triangle are (x+y+ 2) cm, (2x + y) cm and (x +2y+) cm.
For what values of x and y is the triangle equilateral? Also, find the measure of a side of the
triangle.​

Answer 1

Answer:

x=2,y=2 and each side is 8cm.

Explanation:

An equilateral triangle has sides (x+y+2), (2x+y), and (x+2y), all measured in centimetres. How can you find the values of x and y?

Answer

An equilateral triangle has all sides equal.

This means that, x+y+2=2x+y=x+2y. All of the sides must be of same length, in centimetres.

So, to find out the values of x & y, we write the first and last sides equal to each other i.e x+y+2=x+2y, which can also be written as,

2y-y=2

y=2.

So, now we have the value of y.

Now, write down the first and second side to be equal to each other. You're mathematically allowed to do that, cause all sides are equal for equilateral triangle.

Here's what you're gonna do,

x+y+2=2x+y

2x-x=2

So, now we have both values, x=2and y=2.

You can aalso cross check if all sides really are equal or not.

Put the values of x and y in all sides and we have,

x+y+2=8, 2x+y=8, x+2y=8. Hence, we've found the correct values of our variables and all sides are of 8cm in length.