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BARSIC [14]
3 years ago
12

The length of a rectangle is 4n centimeters, and it is twice as long as the width. The perimeter of the rectangle is twice as lo

ng as that of an equilateral triangle. Find the side length of the triangle in terms of n.
PLEASE HELP AND SHOW WORK
Mathematics
1 answer:
sladkih [1.3K]3 years ago
6 0
4n  -  t<span>he length of a rectangle
4n : 2 = 2n  -  </span>the width of a rectangle

P = (4n + 2n) * 2
P = 12n 

12n : 2 = 6n - the perimeter of the equilateral triangle
P = 3a
6n = 3a
a = 6n : 3
a = 2n - <span>the side length of the triangle - answer.</span>
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Answer:

The generalisation she can make from her work is that the other two angles of the quadrilateral are supplementary i.e their sum is 180°

Step-by-step explanation:

We are given the following from what she knows

m∠3=2⋅m∠1... 1

m∠2=2⋅m∠4 ... 2

m∠2+m∠3=360 ... 3

From what is given, we can substitute equation 1 and 2 into equation 3 as shown:

From 3:

m∠2+m∠3=360

Substituting 1 and 2 we will have:

2⋅m∠4 + 2⋅m∠1 = 360

Factor out 2 from the left hand side of the equation

2(m∠4+m∠1) = 360

Divide both sides by 2

2(m∠4+m∠1)/2 = 360/2

m∠4+m∠1 = 180°

Since the sum of two supplementary angles is 180°, hence the generalisation she can make from her work is that the other two angles of the quadrilateral are supplementary i.e their sum is 180°

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