Question

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.

Answer 1

Hello all.

Answer 2

sup

Answer 3

Any ideas?

Answer 4

nope

Answer 5

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

Answer 6

But then I got the wrong answer, as usual

Answer 7

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

Answer 8

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

Answer 9

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.

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

use the distributive law on the denominator

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

Set it equal to zero and solve.

Answer 19

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

Answer 20

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

Answer 21

Thank you for all your help!!

Answer 22

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.

Answer 23

wlcm