how do you work these two problems out?

Question

1. the width of a rectangle is three feet less than the length. The perimeter is 10 ft. Find the width.

2. one angle of a triangle is three times another. the third angle is 45 degrees greater than the smallest. find the measure of the smallest angle.

Answer 1

1. 2 (x+3) + 2 (x) = 10 x= width of rectangle

x = 1
x+3 = 4= length

2. 180 degrees are the sum of the 3 angles

3x + x + (x+45) =180
5x= 135
x = 27 = first angle
3x = 81 second angle
x+45 = 72= third angle

Answer 2

1. the width of a rectangle is three feet less than the length. The perimeter is 10 ft. Find the width.

perimeter of a rectangle is 2*length + 2*width so we can write

10 = 2*L + 2*w

because the width of a rectangle is three feet less than the length you can write l = w+3

10 = 2*L + 2(L-3)
10 = 4L -6
16 = 4L
4 = L

10 = 2*L + 2*w
10 = 2*(4) + 2*w
10 = 8 + 2*w
2 = 2*w
1 = w



2. one angle of a triangle is three times another. the third angle is 45 degrees greater than the smallest. find the measure of the smallest angle.

Since the all the angles added together in a triangle is always 180 we can write an equation

180 = (smallest+45) + smallest + (3*smallest)
180 = 5*smallest +45
135 = 5*smallest

27 = smallest angle

27+45=72= middle angle

3*27=81 = largest angle

Answer 3

#1

2*width + 2*length = perimeter
2(x) + 2 (x+3) =10, where x represents the width of rectangle.
2x + 2x + 6 = 10
4x + 6 = 10
4x = 4
x = 1 ft
length = x+3 = 4 ft

2. The sum of the angles of a triangle is 180 degrees.

x + 3x + (x + 45) =180
5x= 135
x = 27 degrees (first and smallest angle)

3x = 3(27) = 81 degrees (second angle)

Third angle is x+45 = 27 + 45 = 72 degrees

Check answer:
27 + 81 + 72 = 180

Good luck!

Answer 4

#1 is width = 1 and the length = 4. You have to find out what the width would be if it was to be added 3 and multipy those to by 2. 1 + 3 = 4....4 + 1 = 5....5 * 2 = 10 which is the perimeter. uhhhh for #2 i think the total of the angles has to be 180 degrees.....so divide that by 3.... and u get 60... uhhh I dont know this one

Answer 5

1. 10ft = 2x + 2(x - 3)
10ft = 2x + 2x - 6
16ft = 4x
4ft = x, width = 1

2. x + 3x + (45 + x) = 180
5x + 45 = 180
5x = 135
x = 27 degrees <-- shortest

hope that helps

Answer 6

Problem 1

Perimeter formula

P = 2L + 2W

10 = 2L + 2(L - 3)

10 = 2L + 2L - 6

10 = 4L - 6

10 + 6 = 4L - 6 + 6

16 = 4L

16 / 4 = 4L / 4

16 / 4 = L

4 = L

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