Question

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.)

Answer 1

Answer:

143 inches

Step-by-step explanation:

Let the triangle be $s$ inches long.

Then the perimeter of the equilateral triangle will be $s+s+s=3s$ inches.

Let the length of the square also be $l$ inches.

Then the perimeter is $4l$

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

$3s=4l+77$

$\Rightarrow 3s-4l=77..eqn1$

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

So we write $s=l+55$ or $l=s-55...eqn2$

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

$3s-4(s-55)=77$

We expand the bracket to get;

$3s-4s+220=77$

$3s-4s=77-220$

$-s=-143$

$s=143$

Hence  the triangle is 143 inches long.