Hello everyone. Pls kindly help me solve thisproblem. A triangular piece of glas

Question

Hello everyone. Pls kindly help me solve thisproblem. A triangular piece of glass is being cut so that theheight of the triangle is 4 inches shorter than twice the base. Ifthe area of the triangle is 120 square inches, how long is theheight of the triangle? Thanks for your time and assistance. Hello everyone. Pls kindly help me solve thisproblem. A triangular piece of glass is being cut so that theheight of the triangle is 4 inches shorter than twice the base. Ifthe area of the triangle is 120 square inches, how long is theheight of the triangle? Thanks for your time and assistance.

Explanation / Answer

The area of any triangle is base*height/2 They tell you that the area of this triangle is 120 squareinches, so bh/2=120, bh=240 Now they tell you that the height of the triangle is 4 inchesshorter than twice the base. so, the height, h = 2*b-4 so we have: b(2b-4)=240 We have a quadratic equation at hand! We want a 0 in the right side. 2b^2-4b=240 b^2-2b=120 b^2-2b-120=0 Factoring, we get (b-12)(b+10)=0 b=12, or b=-10 Wait. There can only be one solution for the base ofthis triangle. We must realize that the base cannot be anegative number. So, the solution b=-10 is out. The base of this triangleis 12 inches. Yay. Yay. Yay. However, the question asks for the height of thetriangle. Looking back, we remember that h=2b-4 We have b, which is 12! so we get h=2(12)-4=24-4=20inches.

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