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Question

 A rectangle has a base of (x+2) in. and a height of 6 in. A triangle has side lengths of 6 in, (x+4) in and 2x in. if the perimeters of the rectangle and triangle are equal whats the value of x

Answer 1

Here's what we know:

P_r = 2l + 2w

P_t = a + b + c

P_r = P_t

Therefore:

2l + 2w = a + b + c

l = x + 2

w = 6

a = 6

b = x + 4

c = 2x

 

Now we plug the values in for the variables:

2(x + 2) + 2 * 6 = 6 + x + 4 + 2x

Distribute then simplify:

2x + 4 + 12 = 6 + x + 4 + 2x

2x + 16 = 3x + 10

 

Now to isolate x. Start by subtracting 2x:

16 = x + 10

Subtract 10:

6 = x

 

Now to check:

P_r = 2 * 6 + 2 * (6 + 2)

P_r = 12 + 2 * 8

Pr = 12 + 16

P_r = 28

 

P_t = 6 + 6 + 4 + 2 * 6

P_t = 6 + 6 + 4 + 12

P_t = 12 + 12 + 4

P_t = 28

Answer 2

Hi Zane, the perimeter of the triangle is the sum of the three sides, or P_t = 6 + (x + 4) + 2x. The perimeter of the rectangle is equal to two times the length plus two times the width, or P_r = 2(x + 2) + 2x.

 

We know that P_r = P_t

 

Substituting gives:

 

6 + (x + 4) + 2x = 2(x + 2) + 2x

 

6 + x + 4 + 2x = 2x + 4 + 2x

 

Combine like terms on both sides of the equal sign:

 

10 + 3x = 4x + 4

 

Subtract 4 from both sides gives:

 

6 + 3x = 4x

 

Subtract 3x from both sides gives:

 

x = 6.

 

The value of x is 6 inches.

 

To check the results:

 

Substitute 6 for x in 6 + (x + 4) + 2x = 2(x + 2) + 2x.

 

Questions?