Question

A: What is the perimeter of HOUSE?

perimeter of HOUSE =


(round to the nearest hundredth - two decimal places)


B: What is the length of OH?

(round to the nearest thousandth - three decimal places)


C: What is the midpoint of OU?


D: Which is longer, OH or EH?


E: What is the perimeter of the triangle HOU?


perimeter of triangle HOU


(round to the nearest hundredth - two decimal points)

Answer 1

First calculate distances or lengths(Refer to attachment)

A:-

`\\ \sf\longmapsto Perimeter=Sum\:of\:sides`

`\\ \sf\longmapsto 5.3+9+11+9+9.7`

`\\ \sf\longmapsto 15+29`

`\\ \sf\longmapsto 44`

B:-

Refer to the attchment

C:-

`\\ \sf\longmapsto \left((1+4)/(2),(1+6)/(2)\right)`

`\\ \sf\longmapsto \left((5)/(2),(7)/(2)\right)`

D:-

EH>OH

E:-

`\\ \sf\longmapsto Perimeter`

`\\ \sf\longmapsto 9.7+5.3+9`

`\\ \sf\longmapsto 24`

Answer 2

The coordinates of the HOUSE:

• H(-7, 1), O(1, 6), U(4, 1), S(4, -8), E(-7, -8)

Part A

To find the perimeter first find the length of each side:

• OH =
  `√((1 +7)^2+(6-1)^2) = √(64+25) =√(89)` ≈ 9.43 units
• OU =
  `√((4-1)^2+(1-6)^2) = √(9+25) = √(34)` ≈ 5.83 units
• US = 1 - (-8) = 9 units
• SE = 4 - (-7) = 11 units
• EH = 1 - (-8) = 9 units

The perimeter is:

• P = 9.43 + 5.83 + 9 + 11 + 9 = 44.26 units

Part B

• OH = 9.43 units (see part A)

Part C

Use midpoint formula:

• x = (4 + 1)/2 = 2.5
• y = (1 + 6)/2 = 3.5

The point is (2.5, 3.5)

Part D

• OH = 9.43 units > EH = 9 units (see part A)

Part E

• P(ΔHOU) = OH + OU + HU (or SE) = 9.43 + 5.83 + 11 = 26.26 units