Math problems..?

Question

A triangle is 10cm wider than it is tall. The area is 28cm^2. Find the height and base.

Answer 1

A = (1/2)bh

height = x
base = x + 10
Area = 28cm^2

28 = (1/2) (x) (x+10)
28* (2/1) = x (x+10)
56 = x (x + 10)
0 = x^2 + 10x - 56
0 = (x + 14)(x - 4)

2 possible x's:
(x + 14) = 0, and (x - 4) = 0
x = -14, and x = 4
But you can't have a -14 value in cm. So it's x = 4.

height = x = 4 cm.
base = (x + 10) = (4 + 10) = 14 cm



Checking the answers:
A = (1/2)bh
A = (1/2)(4)(14)
28 = 28. Check.

Answer 2

H = height of the triangle
B = Base of the triangle = H + 10

The area of a triangle is (1/2)B*H = (1/2)(H+10)*H = 28
so 56 = H^2 + 10H and H^2 + 10H - 56 = 0
Factor this to get (H + 14)*(H - 4) = 0 so H= either -14 or 4
Since the H can not be negative, the height is 4
And the base is H + 10 or 14

Answer 3

Let the height of the triangle=x
so the base=x+10,& as per given conditions
Area=(1/2)*base*height
or 28=(1/2)*x*(x+10)
or 28*2=x^2+10x
or x^2+10x-56=0
or x^2-4x+14x-56=0
or x(x-4)+14(x-4)=0
or (x+14)(x-4)=0
or x=-14 or x=4
since lenght can"t be negative so x=4
so Base =14 cm &height=4cm

Answer 4

AREA= 1/2 * BASE *HEIGHT
let height isx cm
then base=x+10 cm
28 =1/2 *(x+10) * x
56 = x^2+10x
x^2+10x-56=0
(x+14)(x-4)=0
so x=4 or -14
x=4 as base and height cant b negative
so height is 4 cm
and base is 14cm

Answer 5

assuming a right triangle:

1/2 * b * h = 28

1/2 * (h + 10) * h = 28

.5h *(h + 10) = 28

.5h^2 + 5h = 28

h^2 + 10h - 56 = 0

(h + 14)(h - 4) = 0

h = -14, 4 ---- answer is 4.

b = 4 + 10 = 14

Answer 6

For a triangle, Area 1/2 Base X Height
28 = 1/2 (x+10)(x)
14=x^2 +10x, X^2 +10x -14 = 0
This I cannot solve by inspection, so I'll use the quadratic formula

x = -b+ or - sq. rt. (b^2 - 4ac)
....__________________________
........... 2a

a=+1, b= +10, c=-14

x = -10 + sq. rt. (100 +56)
......._________________ =-10+sq.rt.(156)
..............................................------------
...........2.........................................2
so x = (-10+12.48)/2, = 1.24
OR x = -10 - sq.rt.(100+56) all divided by 2
x = (-10 -12.48)/2, =-22.48/2, =-11.24

The height is 1.24cm, the base is 1.24+10=11.24cm.

You can ignore the -11.24 answer. It makes no sense to have a negative distance, although the -11.24 satisfies the math.