Question

The height of a triangle is 8 centimeters greater than three times its base. The area of the triangle is 128 square centimeters. What is the base of the triangle?

Answer 1

base = 8 cm

Explanation:

Let the base be "b"

Then the height will be "3b + 8"

Therefore use the following to find area:

`\rightarrow \sf (1)/(2) * base * height = area \ of \ triangle`

`\rightarrow \sf (1)/(2) * b* (3b+8)= 128`

`\rightarrow \sf (1)/(2) * b* (3b+8)= 128`

`\rightarrow \sf 3b^2+8b= 128*2`

`\rightarrow \sf 3b^2+8b=256`

`\rightarrow \sf 3b^2+8b-256=0`

`\rightarrow \sf 3b^2+32b-24b-256=0`

`\rightarrow \sf b(3b+32)- 8(3b+32) =0`

`\rightarrow \sf (b- 8)(3b+32) =0`

`\rightarrow \sf b = 8, \ -(32)/(3)`

Therefore "b", base is 8 cm and height = 3(8) + 8 = 32 cm