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?

Question

asked Jul 13, 2023 109k views

1 Answer

Codingmonkey · Answer 1 · 2023-07-18T14:27:46+0000

Answer:

base = 8 cm

Explanation:

Let the base be "b"

Then the height will be "3b + 8"

Therefore use the following to find area:

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

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

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

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

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

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

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

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

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

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