What is the formula for the area of a triangle? A = 1/2 bh, right? If we let b = the length of the base, then the height is b + 7, seven feet greater than the base. Put in the info we have. A = 1/2 bh 15 = 1/2 b(b+7) 30 = b2 + 7b 0 = b2 + 7b - 30 Since we can't factor the equation, it's time to pull out the old quadratic formula. x = -b + √(b2 - 4ac) / 2a = -7 + √49 - 4(1)(-30) / 2 = = -7 + √169 / 2 -7 +13 / 2 = 3 -7 - 13 / 2 = -10 We can't have a negative length, so our base is 3. This makes the height 10. Let's check. 1/2(3)(10) = 15. Good to go!
