Question

The perimeter of the square is equal to the perimeter of the triangle. What are the side lengths of each figure? square: ? units Question 2 triangle shorter side: ? units Question 3 triangle longer sides: ? units, ? units

Answer 1

Answer:

Square: 12 unites

triangle shorter side: 10 units

triangle longer sides: 19 units, 19 units

Step-by-step explanation:

Hello!

First, we make the equations to find the perimeters of each shape by adding all the sides

Square: 4x + 4x + (3x+ 3) + (3x + 3)

Triangle: (7x - 2) + (7x - 2) + (2x + 4)

Since the perimeters are equal we can show that

4x + 4x + (3x+ 3) + (3x + 3) = (7x - 2) + (7x - 2) + (2x + 4)

Now we can solve for x.

Combine like terms

14x + 6 = 16x

Subtract 14x from both sides

6 = 2x

Divide both sides by 2

3 = x

Now we know what x is we can put that into the sides of the shapes

Square

4(x)

Put in x

4(3) = 12

The Square is 12 units

Triangle Short Side

2x + 4

Put in x

2(3) + 4

6 + 4

10

The shorter side of the triangle is 10 units

Triangle Longer Side

7x - 2

Put in x

7(3) - 2

21 - 2

19

The longer sides are 19 units

Hope This Helps!

Answer 2

Answer:

Square= 12 units

Triangle long sides= 19 units

Triamgle short side= 10 units

Step-by-step explanation:

It is a square, so all sides are the same.  That means 3x+3 equals 4x.  What number can be subsituted into x to equal 4?  If x is 3, then 3x+3 would be 3(3)+3.  It equals 12.  4 times 3 is also 12.  It works!  That also means the square's side is 12 units.

Square= 12 units

So, x=3

The triangle's longer sides are 7x-2.  Subsitute x in, which is 3, and you get 7(3)-2.  It equals 19.  The two longer sides of the triangle are the same length, so both are 19 units.

Triangle long sides= 19 units

The triangles shorter side is 2x+4.  Subsitute 3 in for x and you get 2(3)+4.  It equals 10, so the shorter side is 10 units.

Triangle short side= 10 units