Geometry word problem

Question

The height of a triangle is 1 in. more than the base. If the height is increased by 2 in. while the base remains the same, the new area becomes 27 in.²

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

b. Find the area of the original triangle

Answer 1

A = 1/2* B * h

 

   = 1/2*B (B+1)

 

 

 

27 = 1/2*B*(B+3)

 

 54 = B(B+3)

 

 54 = B^2 + 3B

 

0 = B^2 + 3B - 54

 

0 = (   B   +    9 )(B    -     6    )

 

B+9=0 results in negative measures

 

B-6 = 0 ---> B = 6

 

The original triangle has base 6 and height 7, which has area 1/2*6*7 = 21

 

THe new triangle has base 6 and height 9, which has area 12*6*9 = 27