Is this the right answer for a geometry question?

Question

The largest angle of a triangle is three times the smallest angle. The middle angle is 30 degrees more than the smallest angle. Find the number of degrees in each angle.

From what I can see is, the degrees are 75, 75 and 30 but they were looking for a largest angle and 75 is equal to another angel so I'm not sure this might be right or not.

I'm also having trouble with this question:

The length of a rectangle is one inch more than twice the width.

If the perimeter of the rectangle is 92 inches, find the length and width of the rectangle.

I know the formula for the perimeter of a rectangle is adding up all the length and width sides but not sure how to set up the problem in order to solve it.

Answer 1

Hi,

The largest angle of a triangle is three times the smallest angle. The middle angle is 30 degrees more than the smallest angle. Find the number of degrees in each angle.

Let x = degrees in smallest angle

3x = largest angle

x + 30 = middle angle

Angles in a triangle add to 180 so:

x + 3x + x + 30 = 180

5x + 30 = 180

5x = 150

x = 30

3x = 90

x + 30 = 60

The 3 angles are 30, 60, and 90. <==ANSWER

Let x = width

Then length = 1 + 2x

If the perimeter is 92", then 2x + 2(1 + 2x) = 92

2x + 2(1 + 2x) = 92

2x + 2 + 4x = 92

6x + 2 = 92

6x = 90

x = 15 <==WIDTH

1 + 2x = 1 + 2(15) = 31 <==LENGTH

I hope that helps!! :-)

Answer 2

Why didn't you set up an equation?

If smallest angle is x, then the middle angle will be x+30 and the biggest angle will be 3x. Add all of these three and put 180 to the other side of equation and that's it.

Answer 3

Sounds like a 30,60,90 triangle, but let's solve it analytically:

Call the angles A, B & C in order of increasing size

B = A+30

C = 3A

A+B+C = 180

A+ A+30+ 3A = 180

5A = 150

A = 30

B = 60

C = 90

L = 2W+1

2L+2W = 92

4W+2 +2W = 92

6W = 90

W = 15

L = 31

OK, now you can be sure!

Answer 4

1.) The interior angles of a triangle always give a sum of 180-degrees.

Smallest angle = x

Middle angle = x + 30 (the middle is 30 more than the smallest)

Largest angle = 3x (the largest is three times the smallest)

Smallest + Middle + Largest = 180

x + x + 30 + 3x = 180 (combine like terms)

5x + 30 = 180 (subtract 30 from both sides)

5x = 150 (divide both sides by 5)

x = 30 = smallest angle

Middle angle = x + 30  = 30 + 30 = 60

Largest angle = 3x = 3(30) = 90

The angles of the triangle are 30-, 60-, and 90-degrees. <===ANSWER

2.) Perimeter = 2l + 2w = 92 (formula for perimeter of rectangle)

Width = w

Length = l = 2w + 1 (length is one more than twice width)

P = 2l + 2w (substitute 2w + 1 for l)

92 = 2(2w + 1) + 2w (distributive property)

92 = 4w + 2 + 2w (combine like terms)

92 = 6w + 2 (subtract 2 from both sides)

90 = 6w (divide both sides by 6)

15 = w

l = 2w + 1 (substitute 15 for w)

l = 2(15) + 1 (multiply)

l = 30 + 1 (add)

l = 31

Length = 31 inches, Width = 15 inches <===ANSWER

Answer 5

OK, for the first question, draw your triangle. Mark one angle L for large, M for medium and S for small. The large angle is 3 times the small angle, so let's call the small angle x. Put an x next to the S. Put a 3x next to the L. The medium angle is 30+x, so put that in the triangle. Since every triangle's angles add up to 180, you can add those angles and set them up to 180: x+3x+x+30=180

5x+30=180; 5x=150; x=30. The smallest angle, x, is 30. The largest is 3(30)=90. The medium angle is 30+30=60.

draw a rectangle and mark two parallel sides L for length and the other two W for width. Put an x next to each W. For now, you width will be represented by the variable x. Th length is 2 times the width plus one or 2x+1 and you have two of those. Now add up the sides and set that equal to the perimeter, 92: x+x+2x+1+2x+1=92; 6x+2=92; 6x=90; x=15. The width is 15 and the length is 2(15)+1 or 31.

Answer 6

The answer to the first question is 30, 60, 90. Those are the degrees of the angles of the triangle.  

Answer 7

1. 30,60,90

Let the smallest angle be x

The other two angles are 3x and x+30

So x+x+30+3x=180

x=30

Hence 30,60,90

2. Let length be L and Breadth be B

L=2B+1

Perimeter of rectangle is 2(L+B)

Substituting we get

2(3B+1)=92

Hence L=31 B=15