Question

The height of a triangle is 4 feet less than the length of its base, b. The area of the triangle is 30 square feet.

Find the base and the height of the triangle...
.

Answer 1

base(b)=10 and height(h)=6

Explanation:

From the question,

base(b)=x feet

height(h)=(x-4) feet

Area(A)=30 square feet

Now,

We know,

Area of triangle(A)=1/2*b*h

or, 30=1/2*x*(x - 4)

or, 30=1/2*x^2 -4x

or, 30*2=x^2 -4x

or, 60=x^2 -4x

or, 0 = x^2 -4x -60

or, 0 = x^2 +6x - 10x -60

or, 0 = x(x + 6) -10(x + 6)

or, 0 = (x+6) (x-10)

Either,

x+6=0. or, x-10=0

or,x= -6. or, x= 10

Since, the base of the triangle can not be negative number then, x≠ -6feet but x=10feet

Lastly,

Height(h)=X - 4

=10 - 4

=6 feet