The area of a triangle is 44cm^2 and the height is 3cm less than the base. Find the heigh

i need the formula

Area of triangle (1/2) b * h

h = (b - 3)

so,

44 = (1/2)(b)(b - 3) = (1/2)(b^2 - 3b)

solve the quadratic...

b^2 - 3b - 88 = 0

(b - 11)(b + 8) = 0

b = - 8 [extraneous]
or
b = 11 cm

the height is: 8 cm

check

¶

area of triangle=1/2 b * h

base=x cm

height=(x-3)cm

remember the height is 3 cm less than the base and we called the base x. You could have called the base anything you want but x is a more recongnizable variable.

(1/2)*(x)*(x-3)=44

multiply both side by 2.

x(x-3)=88

x^2-3x=88

x^2-3x-88=0

(x-11)(x+8)=0

x=11 x=-8.
Since you have have a negative length then disregard -8 and use 11.

So the base is 11 cm. and the height is (11-3)=8 cm.

To check answer.


(1/2)*(11)*(8)=44.

Area = (h*B)/2 h is the height
B is the base length

b*(b-3)/2=44
b^2-3b-88=0

b = -8 could not be solution

b=11

proof
h=11-3=8
b=11
Area = 11*8/2=44 correct