Question

Find the value of the variables.
Please help!

Answer 1

17. x = 5, y = 3

18. x = 2, y = 7

19. x = 9, y = 4

Explanation:

17. A rhombus has all sides equal

7x - 11 = 24

7x = 35

x = 5

8y = 24

y = 3

18. A rectangle has opposite sides equal

9 = y + 2

y = 7

2y = 7x

2(7) = 7x

x = 2

19. A square has all sides equal

2x - 5 = x + 4

x = 9

3y + 1 = 4(9) - 23

3y + 1 = 13

3y = 12

y = 4

Answer 2

Answers and Step-by-step explanations:

17. This is a rhombus. By definition, all sides of a rhombus are equal. This means that we can set (7x - 11) equal to 24 and solve for x:

7x - 11 = 24

7x = 35

x = 35/7 = 5

We can also set 8y equal to 24 (because all sides are congruent) and solve for y:

8y = 24

y = 24/8 = 3

So, x = 5 and y = 3.

18. This is a rectangle. By definition, opposite sides of a rectangle are equal. This means that we can set 9 and y + 2 equal to each other and 7x and 2y equal to each other:

9 = y + 2 ⇒ y = 9 - 2 = 7

AND

7x = 2y ⇒ 7x = 2 * 7 = 14 ⇒ x = 14/7 = 2

So, x = 2 and y = 7.

19. This is a square. By definition, all sides of a square are congruent. So, we can set 2x - 5 equal to x + 4:

2x - 5 = x + 4

x = 4 + 5 = 9

Now, we can find the side length of the square:

x + 4 = 9 + 4 = 13

So, that means that 3y + 1 equals 13 (because all sides are equal):

3y + 1 = 13

3y = 12

y = 4

So, x = 9 and y = 4.

Hope this helps!