Question

The height of a triangle is 2 units longer than it's base. If the area is 12 square units,what is the length of the base

Answer 1

The vase of the triangle would be x because it is unknown and the height would be x+2 because it is 2 more units than the base the formula for the area of a triangle is (base)(height)% 2 =area so (x)(x+2)%2=12 so then you have 1/2x^2+x=12 at this point I would move the 12 to the other side by subtracting to get 1/2x^2+x-12=0 then I would multiply it all by 2 to get x^2 + 2x-24 from there I would factor to get (x+6)(x-4) and your answers would be x= -6 and 4 and because 6 is negative it would not work because distances are always positive so the base would equal 4

Answer 2

The length of base is 4 unit.

What is area of the triangle?

The area of the triangle is the half of the product of the base and height of that triangle.

Area of the triangle = Δ= (1/2)*base*height

According to asked question,

The height is 2 units greater than base.

So we can assume, base =x

Then height = x+2

Given,

Area of the triangle = 12 square unit

(1/2)*base*height=12 square unit

⇒(1/2)*x*(x+2)=12

⇒x²+2x=24

⇒x²+2x-24=0

⇒x²+6x-4x-24=0

⇒x(x+6)-4(x+6)=0

⇒(x+6)(x-4)=0

⇒x+6=0  or  x-4=0

⇒x=-6  or  x=4

x=-6 will be impossible because the measurement of base cannot be negative.

So x=4

Therefore, the length of base is 4 unit.

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