Houda A.
asked • 07/10/19The base of a triangle is 4 inches more than 4 times the height. If the area is 12 square inches, find the base and the height
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Christina W. answered • 07/10/19
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The base of a triangle is 4 inches more than 4 times the height. If the area is 12 square inches, find the base and the height
The formula for the area of a triangle is A=1/2bh. You are provided the base of 4 inches more than (add) 4 times (multiply) the height). You are also provided the area of 12 inches^2.
What you know:
A = 12 in^2
b= (4h+4)
h= h
So now set up your full equation to solve:
Michael D. answered • 07/10/19
Tutor
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Strong Math and Physical Science Background - Certified Math, physics
The area of a triangle is 1/2 * B * H.
For this problem the base of the triangle is 4 inches more (plus) then 4 times (multiplication) the height of the triangle. Therefore B = 4H + 4 and if we substitute for B we get
Area = 12 = 1/2 * (4H + 4) * H
12 = 1/2 * (4H^2 + 4H)
24= 4H ^ 2 + 4H ==> 4H^2 + 4H - 24 = 0 and H^2 + H - 6= 0
and we can factor into (H + 3)(H - 2) = 0 and H = -3, 2 and since the measurement must be positive,
H =2, and since B = 4 * H + 4 ==> B = 12 and 1/2 BH = 1/2 (12)(2) =12
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Kristopher G.
The area of a triangle is given by A=1/2bh, and from the first line give sus b=4+4h. Therefore we get A=(1/2)(4+4h)h=12. Or (2+2h)h=12. We can simplify further by dividing both sides by 2, and we get (h+1)h=6 or multiplying out h^2+h=6 which gives h^2+h-6=0. This we can factor into (h+3)(h-2)=0 or h=2, or -3. We have a positive hight, therefore, h=2 which gives us a base of b=4+4*2=12. So a base of 12inches. and a hight of 2 inches. We can plug this into the original area formula and see we get an answer of 1207/10/19