The perimeter of an equilateral triangle is 77 inches more than the perimeter of a square, and the side of the triangle is 55 inches longer than the side of the square. find the side of the triangle. (hint: an equilateral triangle has three sides the same length.)

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kudzordzifrancis kudzordzifrancis · Answer 1 · 2019-01-26T16:34:29+01:00

Answer:

143 inches

Step-by-step explanation:

Let the triangle be [tex]s[/tex] inches long.

Then the perimeter of the equilateral triangle will be [tex]s+s+s=3s[/tex] inches.

Let the length of the square also be [tex]l[/tex] inches.

Then the perimeter is [tex]4l[/tex]

It was given that the perimeter of the equilateral triangle is 77 inches more than the perimeter of the square.

So we can write the relation

[tex]3s=4l+77[/tex]

[tex]\Rightarrow 3s-4l=77..eqn1[/tex]

Also, the side of the triangle is 55 inches longer than the side of the square.

So we write [tex]s=l+55[/tex] or [tex]l=s-55...eqn2[/tex]

We put equation (2) into equation (1) to get;

[tex]3s-4(s-55)=77[/tex]

We expand the bracket to get;

[tex]3s-4s+220=77[/tex]

[tex]3s-4s=77-220[/tex]

[tex]-s=-143[/tex]

[tex]s=143[/tex]

Hence the triangle is 143 inches long.