Solve for Trapezoid base

[irish634]

Hello,

I apologize if this is in the wrong section.

I need to be able to solve for one base of a trapezoid when the only known parameters are: the perimeter, the height, and the opposite base.

I have been able to accomplish solving for the height when I have the 2 bases and the perimeter by solving the hypotenuse:
H = {[(P - (LB + SB))/2]^2-[(LB-SB)^2/4]}^0.5 where:

H = height
P = perimeter
LB = long base
SB = short base

Also, I am able to solve for the bases when I have the area of the trapezoid, but in this case, I only have the perimeter. I am struggling with my question and not really sure how to go about solving for the bases.

This is for work, and if anyone can point me in the right direction I would appreciate it.

Thank you,
Craig

 

[Deleted member 4993]

Hello,

I apologize if this is in the wrong section.

I need to be able to solve for one base of a trapezoid when the only known parameters are: the perimeter, the height, and the opposite base.

I have been able to accomplish solving for the height when I have the 2 bases and the perimeter by solving the hypotenuse:
H = {[(P - (LB + SB))/2]^2-[(LB-SB)^2/4]}^0.5 where:

H = height
P = perimeter
LB = long base
SB = short base

Also, I am able to solve for the bases when I have the area of the trapezoid, but in this case, I only have the perimeter. I am struggling with my question and not really sure how to go about solving for the bases.

This is for work, and if anyone can point me in the right direction I would appreciate it.

Thank you,
Craig

Do you know Newton's method of finding roots of functions?

 

[irish634]

I don't know it but I will look it up. Thank you

Edit: So basically I need to solve for these iteratively?

 

[Denis]

I need to be able to solve for one base of a trapezoid when the only known parameters are: the perimeter, the height, and the opposite base.

Easy enough; assume perimeter = 30, height = 4, and short base = 7:

p = perimeter (given) ; 30
b = height (given) ; 4
w = short base (given) ; 7

c = hypotenuse sides
w + 2a = long base

2a + 2c + 2w = p
2a + 2c + 14 = 30
a + c = 8
c = 8 - a

a^2 + b^2 = c^2
a^2 + 16 = (8 - a)^2
a = 3

long base = w + 2a = 7 + 6 = 13

Follow?

I used 2 a-b-c or 3-4-5 right triangles and sat 'em on sides a, 7 apart, sides b facing each other...
That was to illustrate; but they'll all work out similarly.

 

[irish634]

a^2 + 16 = (8 - a)^2
a = 3

Follow?

Thank you Denis. I follow up to this point. I'm not sure how you reduced that to a = 3. I think once I grasp this part, the rest 'should' fall into place for me.

 

[Deleted member 4993]

a^2 + 16 = (8 - a)^2
a = 3

Follow?

Thank you Denis. I follow up to this point. I'm not sure how you reduced that to a = 3. I think once I grasp this part, the rest 'should' fall into place for me.

If you expand (8-a)[sup:3psde8v8]2[/sup:3psde8v8] and collect "like" terms - you should get an equation - and solution of that equation is .....

 

[Deleted member 4993]

I need to be able to solve for one base of a trapezoid when the only known parameters are: the perimeter, the height, and the opposite base.

Easy enough; assume perimeter = 30, height = 4, and short base = 7:

p = perimeter (given) ; 30
b = height (given) ; 4
w = short base (given) ; 7

c = hypotenuse sides <<< Denis, are you assuming that the "slant" sides are equal (=c) - i.e. - you have an isosceles trapezoid?
w + 2a = long base

2a + 2c + 2w = p
2a + 2c + 14 = 30
a + c = 8
c = 8 - a

a^2 + b^2 = c^2
a^2 + 16 = (8 - a)^2
a = 3

long base = w + 2a = 7 + 6 = 13

Follow?

I used 2 a-b-c or 3-4-5 right triangles and sat 'em on sides a, 7 apart, sides b facing each other...
That was to illustrate; but they'll all work out similarly.

 

[irish634]

c = hypotenuse sides <<< Denis, are you assuming that the "slant" sides are equal (=c) - i.e. - you have an isosceles trapezoid?

My apologies for not stating that. Yes, my assumption is that I have an isosceles trapezoid.

 

[Denis]

a^2 + 16 = (8 - a)^2
a = 3 Follow?

Thank you Denis. I follow up to this point. I'm not sure how you reduced that to a = 3. I think once I grasp this part, the rest 'should' fall into place for me.

a^2 + 16 = (8 - a)^2
a^2 + 16 = 64 - 16a + a^2
16a = 64 - 16
16a = 48
a = 48/16 = 3

I "assumed" isosceles, since an answer calculated directly seemed possible from the nature of the question.