MBrecht92
The base of a triangle exceeds its height by 17 inches. If its area is 55 square inches, find the base
and height of the triangle.



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MBrecht92
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Hello all.

prettyboy20202
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sup

MBrecht92
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Any ideas?

prettyboy20202
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nope

MBrecht92
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I thought I should set up the problem this way: 55 = 1/2(h+h+17)

MBrecht92
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But then I got the wrong answer, as usual

mathstudent55
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let h = height, then
let b = base = h + 17
Area of triangle: A = (bh)/2
55 = (h + 17)h/2

MBrecht92
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Right, exactly..so 55 = 2h+17/2, and thus h+17/2 = 55. Then, 55*2 = h+17

mathstudent55
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Your're close, but the formula for the area of a triangle is the base times the height over 2, not the base plus the height over 2.

helder_edwin
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right
\[ \large 55=\frac{(h+17)\cdot h}{2} \]

MBrecht92
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Um...but I already multiplied the b by the h. It's just that here, b = h + 17

mathstudent55
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it's not (2h + 17)/2 = 55, it's
(h^2 + 17h)/2 = 55

helder_edwin
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use the distributive law on the denominator

helder_edwin
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\[ \large 55=\frac{h^2+17h}{2} \]

MBrecht92
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Okay. So you end up with h^2 + 17h = 110

MBrecht92
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Then...h^2+17h110

mathstudent55
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Right. Now subtract the 110 to the left and solve the quadratic eq.

mathstudent55
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Set it equal to zero and solve.

MBrecht92
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(x+22)(x5) = 0, x = 22, 5

MBrecht92
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Sorry...I meant h. So h = 5, and then b = (5) + 17 = 22

MBrecht92
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Thank you for all your help!!

mathstudent55
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Not x, but h. Now you have h = 22 or h = 5. A negative number is meaningless as the height of a triangle, so dicard it. yes, you got it.

mathstudent55
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wlcm