# Help with a geometry word problem! Triangle Side lengths! Suppose a chair has a seat that's an isosceles triangle and the congruent sides measure 1.5 ft. A second chair has a triangular seat w/a...

Help with a geometry word problem! Triangle Side lengths!

Suppose a chair has a seat that's an isosceles triangle and the congruent sides measure 1.5 ft. A second chair has a triangular seat w/a perimeter of 5 1/10 ft, and it's congruent to the first seat. What is a side length of the second seat?

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### 3 Answers

Given:

Chair 1: isoscale traingle with sides:

1.5 , 1.5 and x.

Chair 2: congruent to chair 1:

Then, sides for chair1 = sides for chair 2.

also , Perimeter for chair1 = perimeter for chair 2.

Given perimeter for chair 2= 5 1/10 = 5.1

Then:

perimeter of chair1 = perimeter of chair 2= 1.5+ 1.5 + x = 5.1

==> 3 + x = 5 1/10

==>** x= 2 1/10= 2.1**

**Then the third side of the triangles = 2**

If you have stated the question properly, then all you have to remember is that congruent triangles have both sides and angles that are congruent. This is as opposed to similar triangles that have congruent angles, but not necessarily sides.

If these two triangles are congruent, they both have the same side lengths and the same total perimeter. Given that, we can see that the sides of the second triangle (and the first) are 1.5 feet, 1.5 feet and 2.1 feet.

The reason for this is that the perimeter of a triangle is the sum of all its sides. We know that two of the sides are 1.5 feet each. Those two sides, then, come out to 3.0 feet in length. If the perimeter of the whole triangle is 5.1 feet, then the remaining side must be 2.1 feet.

The seat of the first chair is an isosceles triangle with its equal sides measuring 1.5 feet.

The sides of the seat of the second chair are congruent with the sides of the first chair. Therefore the seat of the second chair is also isosceles. So the seat of the second chair has two sides each measuring 1.5 feet. As per the given information the seat of the second chair has a perimeter 5 1/10 ft. Thus the second chair has the another side which should measure 5 1/10 ft - 2*1.5ft = (5.1 - 3) ft = 2.1 ft.

So the measurents of the sides of the second chair are: 1.5 feet, 1.5 feet and the other side 2.1 feet.