the height of a triangle is 1 cm than the length of its base. its area is 15 cm to the power of 2

Question

the height of a triangle is 1 cm than the length of its base. its area is 15 cm to the power of 2. what is the height?

Answer 1

the height is 1 cm greater than or less than its base ???

suppose greater...

A=(1/2)(b)(h)

15=(1/2)(b)(b+1)

multiply both sides by 2

30=b(b+1)

30=b²+b

b²+b-30=0

factor

(b+6)(b-5)=0

b-5=0

b=5 cm

b+1=6 cm (height)

suppose less...

15=(1/2)(b)(b-1)

30=b(b-1)

30=b²-b

b²-b-30=0

(b-6)(b+5)=0

b-6=0

b=6 cm

b-1=5 cm (height)

Answer 2

A=(1/2)*b*h

A=15 cm²

Since the height of the triangle is 1 cm more than the length of its base, let base = x and the height = x + 1

So, b=x, h=x+1

Plug given materials into the formula:

15=(1/2)(x)(x+1) and

15=(1/2)(x²+x)

Multiply both sides by 2 to get rid of the fraction:

30=x²+x

Move the 30 over so you can factor:

x²+x-30=0

Factor:

(x+6)(x-5)=0

So x=-6 or x=5

Since length can't be negative, we know x has to equal 5

From the beginning, we set b=x=5 so h=x+1=5+1=6

So the height is 6 cm