The area of a triangle of aluminum sheeting is 120in^2. The base of the triangle is 4 inches more then twice the height.

Question

need the answer quick please help

Answer 1

B = base

H = height

 

Area of a triangle is

(B * H) / 2 = 120

B*H = 240

 

From the 2nd sentence:

B = 2*H + 4

 

Use the 2nd equation to replace B in the 1st equation:

(2*H + 4)*H = 240

 

Expand and solve for H:

2H^2 + 4H = 240

H^2 + 2H = 120

H^2 + 2H - 120 = 0     <<standard quadratic form>>

(H + 12)(H - 10) = 0

 

H = -12 or +10  <<the positive solution is the only one that's useful here>>

 

B = 240 / H = 24

Answer 2

area=(1/2)*base*height

A=(1/2)(b)(h)

base=4+2*height

b=4+2h

substitute 4+2h for b in the formula A=(1/2)(b)(h)

A=(1/2)(4+2h)(h)

A=(2+h)(h)

120=(2+h)(h)

120=2h+h²

h²+2h-120=0

factor

(h+12)(h-10)=0

h-10=0

h=10 inches

b=4+2(10)=4+20=24 inches