Question

Find the perimeter of the image below: Figure QRSTU is shown. Q is at 2, 0. R is at 4, 5. S is at 8, 7. T is at 6, 4. U is at 10, 3. 25.8 units 26.1units 27.5 units 28.6 units

Answer 1

The correct answer should be B which is 26.1

The full answer is 26.16

Answer 2

Hence, the perimeter of the figure is:

(√29+ 2√5 +√13+ √17+√73) units=26.1 units.

Explanation:

The perimeter of the figure is the length of all the line segments.

i.e. Line segment QR,RS,ST,TU and QU.

We know that the distance between two points (a,b) and (c,d) is given as:

`√((c-a)^2+(d-b)^2)`.

• Length of segment Q(2,0)R(4,5) is equal to the distance between these the coordinates of these vertex.

i.e. distance between (2,0) and (4,5) is:

`√((4-2)^2+(5-0)^2)\\\\=√(2^2+5^2)\\\\=√(4+25)\\\\=√(29)`

Hence length of line segment QR is: √29 units.

• Length of segment R(4,5)S(8,7) is equal to the distance between these the coordinates of these vertex.

i.e. the distance between (4,5) and (8,7) is:

`√((8-4)^2+(7-5)^2)\\\\=√(4^2+2^2)\\\\=√(16+4)\\\\=√(20)=2√(5)`

Hence length of line segment RS is: 2√5 units.

• Length of segment S(8,7)T(6,4) is equal to the distance between these the coordinates of these vertex.

i.e. the distance between (8,7) and (6,4) is:

`√((8-6)^2+(7-4)^2)\\\\=√(2^2+3^2)\\\\=√(4+9)\\\\=√(13)`

Hence length of line segment RS is: √13 units.

• Length of segment T(6,4)U(10,3) is equal to the distance between these the coordinates of these vertex.

i.e. the distance between (6,4) and (10,3) is:

`√((10-6)^2+(3-4)^2)\\\\=√(4^2+(-1)^2)\\\\=√(16+1)\\\\=√(17)`

Hence length of line segment RS is: √17 units.

• Length of segment U(10,3)Q(2,0) is equal to the distance between these the coordinates of these vertex.

i.e. the distance between (10,3) and (2,0) is:

`√((10-2)^2+(3-0)^2)\\\\=√(8^2+3^2)\\\\=√(64+9)\\\\=√(73)`

Hence length of line segment RS is: √73 units.

Hence, the perimeter of the figure is:

(√29+ 2√5 +√13+ √17+√73) units=26.1 units