## MBrecht92 2 years ago 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.

1. MBrecht92

Hello all.

2. prettyboy20202

sup

3. MBrecht92

Any ideas?

4. prettyboy20202

nope

5. MBrecht92

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

6. MBrecht92

But then I got the wrong answer, as usual

7. mathstudent55

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

8. MBrecht92

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

9. 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.

10. helder_edwin

right $\large 55=\frac{(h+17)\cdot h}{2}$

11. MBrecht92

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

12. mathstudent55

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

13. helder_edwin

use the distributive law on the denominator

14. helder_edwin

$\large 55=\frac{h^2+17h}{2}$

15. MBrecht92

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

16. MBrecht92

Then...h^2+17h-110

17. mathstudent55

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

18. mathstudent55

Set it equal to zero and solve.

19. MBrecht92

(x+22)(x-5) = 0, x = -22, 5

20. MBrecht92

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

21. MBrecht92

Thank you for all your help!!

22. 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.

23. mathstudent55

wlcm