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Maru [420]
3 years ago
8

6. The perimeter of a parallelogram is 100 meters. The width of the parallelogram is 4 meters less than its length. Find the len

gth and width of the parallelogram.​
Mathematics
1 answer:
Ierofanga [76]3 years ago
5 0

Answer:

x = 23, and y = 27.

Step-by-step explanation:

Lets say,

x = width

y = length

this means,

x(2) + y(2) = 100

It also says that the width is 4 meters less than the length.

if we put that into equation form it would look like this,

y - 4 = x

using these 2 equations, we can use the subustusion method to find the x.

x(2) + y(2) = 100

turns in to this :

step 1.     (y - 4) (2) + y(2) = 100 - given

step 2.      2y -8 + 2y = 100 -  distribute

step 3.      4y -8 = 100 - Combine like terms

step 4.       4y  = 108 - Get rid of the 8

step 5        4y/4  = 108 /4 - divide

step 6 .          y = 27

So if y is 27, then

x(2)  +  27(2) = 100

x(2) + 54 = 100

100 - 54 = 46, so x(2) is 46, but to get x, we need to divide 46 by 2, since x multiplied by 2 equals 46.

46  / 2 = 23 = x

so x = 23, and y = 27.

and the rule that y - 4 = x still applies, since 27 - 4 = 23.

I hope this wasn't confusing! It did take a long time tho.

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olga2289 [7]

Answer:

  1. OT⊥BA;T is the midpoint of BA-------Given
  2. ∠BTO and ∠ATO are right angles ---Definition of perpendicular lines
  3. ∠BTO≅∠ATO---------------------------------All right angles are congruent
  4. T is the midpoint of BA------------------ Given
  5. TA≅TB-------------------------------------------Definition of midpoint
  6. TO≅TO------------------------------------------Reflexive
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Step-by-step explanation:

Given that OT⊥BA and T is the midpoint of BA

As OT⊥BA,

∠BTO and ∠ATO are right angles (Definition of perpendicular lines)

⇒∠BTO≅ ∠ATO (All right angles are congruent)

T is the midpoint ofBA (given)

⇒TA≅TB (Definition of midpoint)

TO≅TO (Reflexive)

Therefore, ΔBOT≅ΔAOT (by SAS criteria ):

conditions:

  • BT=AT(side)
  • ∠BTO=∠ATO(angle)
  • TO=TO(side)
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Answer:

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Let x = number of $25 tickets

Let y = number of $50 tickets

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25x + 50y = 50,000

Equation of the number of tickets:

x + y = 1250

Answer:

25x + 50y = 50,000

x + y = 1250

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