Can anyone help me with this geometery question PLEASE!!?

Question

Can anyone figure this one out.. it has me stumped... please please.. this is the last one and I can not figure it out at all... thank you all for all your other help..

The base of a triangle is 7 cm greater that the height. The area is 39 cm^2. Find the height and the length of the base.

The height is ??? cm.

The length is ?? cm.

THANK YOU SO MUCH!!

Answer 1

The area of the triangle is (base*height)/2. In this case that would mean that, using H for height:

H(H+7)/2=39
H(H+7) = 78

Solve for H however you want - you'll get H=6. This gives us the answer:

height = 6cm
base = 13cm

Answer 2

First write out the given.
Area of Triangle is (base*height)/2
so 39 = (base*height)/2

now
base = height + 7
substitue base equation into area you get
78 = (h+7)*h

multiplying through, collecting terms on right sight of equation you get h^2 + 7*h - 78 = 0 Solving this quadradic, you get two terms, one which is negative, so we disregard since there is no such thing as negative height. I get h = 6cm
substitute h = 6 into the base equation and i get base = 13 cm

Answer 3

Use a system of equations...

A = bh/2
b = h + 7

Substitute...

39 = [(h+7)(h)]/2
39 = (h^2 + 7h)/2

h^2 + 7h - 78 = 0

Argh that's sort of hard >__<
Now you must factor...

h^2 + 13h - 6h - 78 = 0
h(h + 13) -6(h +13) = 0
(h - 6)(h + 13) = 0

So the height can equal -13 or 6, since height can't be negative... it's 6.

The base is 6 + 7 = 13.

Answer 4

The height is x.
the base is (x+7) -- al in centimetres, of course

The area:
(1/2)*base*height
(1/2)*x*(x+7) = 39 cm^2

(1/2)(x^2 + 7x) =39
x^2 + 7x = 78
x^2 +7x - 78 = 0

Time to bring out the quadratic formula:

x = [ -7 +/- SQRT( 49 + 312) ] / 2

one value of x will be negative (drop it),
the other will be positive (choose it).

Then check the values (by doing the calculation with your answer instead of x)

Answer 5

Area of triangle = bh/2
(h+7)h/2=39
h^2+7h=78
h=6
So 6*13/2=39

Answer 6

a=(1/2)*height*base.
Assume height is x cm --> base=(x+7)
x(x+7)=39*2
x^2+7x-78=0
x=(1/2)[-7 (+/-)19]
=(1/2)(12) only positive root admissible
=6
height=6cm, base=13cm

Answer 7

assuming a right triangle:
The base is 6.
The height is 13.
Check: The area is (6X13)/2 = 39.
QED.

Answer 8

continuing off of daniel, the base is 13 (just in case you couldn't figure it out)