A certain rectangle has a perimeter of
30 units and an area of 56 square units
Two of the vertices have coordinates
and . Which two
coordinates could be the other two
vertices of the rectangle?
(A)
(8)
©
(D)

Ask by Ramos Kelly. in the United States

Mar 30,2025

Question

A certain rectangle has a perimeter of
30 units and an area of 56 square units
Two of the vertices have coordinates
and . Which two
coordinates could be the other two
vertices of the rectangle?
(A)
(8)
©
(D)

Ask by Ramos Kelly. in the United States

Mar 30,2025

UpStudy AI · Accepted Answer

We are given a rectangle with a perimeter of $$30$$ units and an area of $$56$$ square units. Two vertices are given as  
$$
(-8,5) \quad \text{and} \quad (0,5).
$$

**Step 1. Find the length of the side between the given vertices.**

The two points lie on a horizontal line, so their distance is the difference in the $$x$$-coordinates:
$$
0 - (-8) = 8.
$$
Thus, one side of the rectangle has length $$8$$.

**Step 2. Determine the other side’s length using the perimeter.**

For a rectangle with side lengths $$l$$ and $$w$$, the perimeter is
$$
2(l+w)=30.
$$
Since one side $$l=8$$, we have:
$$
2(8+w)=30 \quad \Longrightarrow \quad 8+w=15 \quad \Longrightarrow \quad w=7.
$$

**Step 3. Verify using the area.**

The area is given by:
$$
\text{Area}=l \times w = 8 \times 7 = 56.
$$
This agrees with the information given.

**Step 4. Determine possible positions for the other two vertices.**

Since the vertices $$(-8,5)$$ and $$(0,5)$$ form a horizontal side of length $$8$$, the other two vertices must be directly above or below these points by a vertical distance of $$7$$.

- If the rectangle extends upward, the corresponding $$y$$-coordinate will be:
  $$
  5+7=12,
  $$
  so the other vertices would be $$(-8,12)$$ and $$(0,12)$$.

- If the rectangle extends downward, the corresponding $$y$$-coordinate will be:
  $$
  5-7=-2,
  $$
  so the other vertices would be $$(-8,-2)$$ and $$(0,-2)$$.

**Step 5. Match with the given choices.**

The answer choices provided are:
- (A) $$(-8,-2)$$
- (B) $$(0,12)$$
- (C) $$(-8,2)$$
- (D) $$(0,-2)$$

To form a proper rectangle, the two additional vertices must share one $$x$$-coordinate with the given vertices. The pair $$(-8,-2)$$ and $$(0,-2)$$ forms a consistent set of vertices with the side $$(-8,5)$$ to $$(0,5)$$.

Thus, the other two vertices of the rectangle can be  
$$
\boxed{(-8,-2) \text{ and } (0,-2)}.
$$
The other two vertices of the rectangle are $$(-8, -2)$$ and $$(0, -2)$$.

A certain rectangle has a perimeter of
30 units and an area of 56 square units
Two of the vertices have coordinates
and . Which two
coordinates could be the other two
vertices of the rectangle?
(A)
(8)
©
(D)

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A certain rectangle has a perimeter of 30 units and an area of 56 square units Two of the vertices have coordinates and . Which two coordinates could be the other two vertices of the rectangle? (A) (8) © (D)

Solución de inteligencia artificial de Upstudy

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Latest Geometry Questions

A certain rectangle has a perimeter of
30 units and an area of 56 square units
Two of the vertices have coordinates
and . Which two
coordinates could be the other two
vertices of the rectangle?
(A)
(8)
©
(D)