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The height of a triangle is 5 less its base. The area of the triangle is 42 square inches. Create an equation that represents this situation. Use the concept of finding roots/zeros to find the base and height of the triangle.

Feb 27, 2019
edited by Guest  Feb 27, 2019

#2
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Area of a triangle = 1/2 base x height    b = b    h = b-5    area = 42 in^2  (given)

42 = 1/2   b (b-5)

84 = b^2-5b

b^2-5b - 84 = 0    factor    (or use quadratic formula)

(b+7)(b-12)= 0      so b  can =  12 or -7      toss out -7 because you can't have a negative length

so b = 12

h = b-5 = 12-5 = 7

Check:  Area  = 1/2 b h = 1/2  12  7  = 42    Correct !

Feb 27, 2019
edited by ElectricPavlov  Feb 27, 2019

#1
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Hi!

So what you need to know for this, is the formula for the area of a triangle which is 1/2 x base x height

The area of the triangle is given to you.

So  42 = 1/2 x b x 5-b

Then after that, you can probably use Algebra to find out the answer. This would require the use of quadratic roots and zeroes, like you said. So you would find answers that look like this (x-2)=0- and (x+2)=0. I'm not saying this is exactly what you'll get, but something along the lines of that.

Then you just solve! :) Hope this helps... I tried L:

Feb 27, 2019
#2
+2

Area of a triangle = 1/2 base x height    b = b    h = b-5    area = 42 in^2  (given)

42 = 1/2   b (b-5)

84 = b^2-5b

b^2-5b - 84 = 0    factor    (or use quadratic formula)

(b+7)(b-12)= 0      so b  can =  12 or -7      toss out -7 because you can't have a negative length

so b = 12

h = b-5 = 12-5 = 7

Check:  Area  = 1/2 b h = 1/2  12  7  = 42    Correct !

ElectricPavlov Feb 27, 2019
edited by ElectricPavlov  Feb 27, 2019
#3
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Thank you so much! Guest Feb 27, 2019