Word Problem

Question

An isosceles triangle is one in which two of the sides are the same length. The perimeter of an isosceles triangle is 63 cm. If the length of the congruent is 4 times the length of the third side, find the dimensions of the triangle

Answer 1

Please explain what do you mean by cogruent because i have studied congruent triangle but not the congruent of a triangle.

I will try to solve it as follows. x = length of third side not equal, y=length of one of the two equal sides.

So: 2Y + x = 63

and y = 4x

plugging the 2nd equation in the first, we obtain

8x + x =63

9x = 63 and x = 7cm

Y=28 cm

Test 56+7=63

Then what you call the congruent is the sides that are equal but the definition of congruent triangle is the one that has exactly equal the correspondent sides to another and the angles as well.

 

 

 

Answer 2

Since the triangle is isosceles, we know that two sides are equal length. They then tell us that the congruent side is 4 times the length of the third side. 

 

we will let:

 

x = congruent side

y = the third side

 

    /\

x /  \ x

  /    \

   y

 

We have two congruent sides, therefore:

 

x + x + y = 63

 

2x + y = 63

 

since the length of the congruent is 4 times the length of the third side:

x = 4y

 

substitute 4y for x:

 

4(2x) + y = 63

8x + y = 63

 

9y = 63

 

y = 7, this is the length of the third side

4y = 28, this is the length of one of the congruent sides

 

total dimensions:

 

28 + 28 + 7 = 63