Write as an equation: A triangle...

Question

Write as an equation: A triangle has two equal sides and a third side that is 15cm long. How long is each of the equal sides if the perimeter is 50?

Answer 1

Since one side of the triangle is 15 cm, the remaining two EQUAL sides added to the 15 cm side = 50 cm.

 

2 x + 15 = 50.

 

2 x = 50 - 15

 

Can you solve for x?

Answer 2

The perimeter (P) is the sum of the lengths of the three sides of the triangle.  Let's label the sides a, b, and c.  The perimeter is:

 

P = a + b + c

• The triangle has two equal sides, so a = b
• The third side is 15 cm long
• The perimeter is 50 cm

 

P = a + b + c

50 = a + b + 15

 

Since a=b, replace b with a

 

50 = a + a + 50

50 = 2a + 15

35 = 2a

17.5 = a

 

Since a = b and a = 17.5 cm, b = 17.5 cm

 

Check:

     P = a + b + c

     50 = 17.5 + 17.5 + 15

     50 = 50

     Check!

Answer 3

Here's what we know:

P = a + b + c (the perimeter is the three sides added up)

P = 50 (Perimeter is 50 cm)

a = b (2 sides are the same length)

c = 15

 

Now to plug in the values:

a + a + 15 = 50

2a + 15 = 50

Subtract 15:

2a + 15 - 15 = 50 - 15

2a = 35

Divide by 2:

2a / 2 = 35 / 2

a = 17.5

b = a = 17.5

 

Check:

17.5 + 17.5 + 15 = 50

35 + 15 = 50

50 = 50