Studdy AI Logo
Math

QuestionFind the total length of painter's tape needed for walls ABCDABCD with A(−5,−1)A(-5,-1), B(6,3)B(6,3), C(6,−5)C(6,-5), D(−5,−5)D(-5,-5).

Studdy Solution

STEP 1

Assumptions1. The walls are represented by quadrilateral ABC. The coordinates of the vertices are A(-5,-1), B(6,3), C(6,-5), and D(-5,-5)
3. Each interval on the coordinate plane represents one foot4. The walls are congruent trapezoids5. We need to find the total length of the edges of both walls

STEP 2

First, we need to find the lengths of the four sides of the trapezoid. We can do this by using the distance formula between two points in a coordinate plane.
The distance formula is given byd=(x2−x1)2+(y2−y1)2d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}

STEP 3

Let's calculate the length of side AB. The coordinates of points A and B are A(-5,-1) and B(6,3) respectively.
AB=(6−(−5))2+(3−(−1))2AB = \sqrt{(6 - (-5))^2 + (3 - (-1))^2}

STEP 4

Calculate the length of side AB.
AB=(6−(−))2+(3−(−1))2=121+16=137AB = \sqrt{(6 - (-))^2 + (3 - (-1))^2} = \sqrt{121 +16} = \sqrt{137}

STEP 5

Now, let's calculate the length of side BC. The coordinates of points B and C are B(,3) and C(,-5) respectively.
BC=(−)2+(3−(−5))2BC = \sqrt{( -)^2 + (3 - (-5))^2}

STEP 6

Calculate the length of side BC.
BC=(6−6)2+(3−(−5))2=0+64=64=8BC = \sqrt{(6 -6)^2 + (3 - (-5))^2} = \sqrt{0 +64} = \sqrt{64} =8

STEP 7

Next, let's calculate the length of side CD. The coordinates of points C and D are C(6,-5) and D(-5,-5) respectively.
CD=((−5)−6)2+((−5)−(−5))2CD = \sqrt{((-5) -6)^2 + ((-5) - (-5))^2}

STEP 8

Calculate the length of side CD.
CD=((−5)−6)2+((−5)−(−5))2=121+0=121=11CD = \sqrt{((-5) -6)^2 + ((-5) - (-5))^2} = \sqrt{121 +0} = \sqrt{121} =11

STEP 9

Finally, let's calculate the length of side DA. The coordinates of points D and A are D(-5,-5) and A(-5,-) respectively.
DA=((−5)−(−5))2+((−5)−(−))2DA = \sqrt{((-5) - (-5))^2 + ((-5) - (-))^2}

STEP 10

Calculate the length of side DA.
DA=((−5)−(−5))2+((−5)−(−))2=0+16=16=4DA = \sqrt{((-5) - (-5))^2 + ((-5) - (-))^2} = \sqrt{0 +16} = \sqrt{16} =4

STEP 11

Now that we have the lengths of all the sides of the trapezoid, we can find the total length of painter's tape needed for one wall. This is the sum of the lengths of the four sides.
Total length for one wall=AB+BC+CD+DATotal\, length\, for\, one\, wall = AB + BC + CD + DA

STEP 12

Plug in the lengths of the sides to calculate the total length for one wall.
Total length for one wall=137+8+11+4Total\, length\, for\, one\, wall = \sqrt{137} +8 +11 +4

STEP 13

Calculate the total length for one wall.
Total length for one wall=137+8+11+≈11.7+8+11+=34.7Total\, length\, for\, one\, wall = \sqrt{137} +8 +11 + \approx11.7 +8 +11 + =34.7

STEP 14

Since there are two walls, we need to double the total length for one wall to get the total length of painter's tape needed.
Total length of painter′s tape=2timesTotal length for one wallTotal\, length\, of\, painter's\, tape =2 \\times Total\, length\, for\, one\, wall

STEP 15

Plug in the total length for one wall to calculate the total length of painter's tape needed.
Total length of painter′s tape=2times34.7Total\, length\, of\, painter's\, tape =2 \\times34.7

STEP 16

Calculate the total length of painter's tape needed.
Total length of painter′s tape=2times34.=69.4Total\, length\, of\, painter's\, tape =2 \\times34. =69.4

STEP 17

Since the length of painter's tape needed is to be rounded to the nearest whole foot, we round69.4 to69.
Aida and Marco need approximately69 feet of painter's tape to cover the edges of both walls.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord