anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Hello all.
anonymous
  • anonymous
sup
anonymous
  • anonymous
Any ideas?

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More answers

anonymous
  • anonymous
nope
anonymous
  • anonymous
I thought I should set up the problem this way: 55 = 1/2(h+h+17)
anonymous
  • anonymous
But then I got the wrong answer, as usual
mathstudent55
  • mathstudent55
let h = height, then let b = base = h + 17 Area of triangle: A = (bh)/2 55 = (h + 17)h/2
anonymous
  • anonymous
Right, exactly..so 55 = 2h+17/2, and thus h+17/2 = 55. Then, 55*2 = h+17
mathstudent55
  • mathstudent55
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
  • helder_edwin
right \[ \large 55=\frac{(h+17)\cdot h}{2} \]
anonymous
  • anonymous
Um...but I already multiplied the b by the h. It's just that here, b = h + 17
mathstudent55
  • mathstudent55
it's not (2h + 17)/2 = 55, it's (h^2 + 17h)/2 = 55
helder_edwin
  • helder_edwin
use the distributive law on the denominator
helder_edwin
  • helder_edwin
\[ \large 55=\frac{h^2+17h}{2} \]
anonymous
  • anonymous
Okay. So you end up with h^2 + 17h = 110
anonymous
  • anonymous
Then...h^2+17h-110
mathstudent55
  • mathstudent55
Right. Now subtract the 110 to the left and solve the quadratic eq.
mathstudent55
  • mathstudent55
Set it equal to zero and solve.
anonymous
  • anonymous
(x+22)(x-5) = 0, x = -22, 5
anonymous
  • anonymous
Sorry...I meant h. So h = 5, and then b = (5) + 17 = 22
anonymous
  • anonymous
Thank you for all your help!!
mathstudent55
  • mathstudent55
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
  • mathstudent55
wlcm

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