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McGraw Hill Integrated II, 2012
MH
McGraw Hill Integrated II, 2012 View details
6. Solving x^2+bx+c=0
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Exercise 30 Page 49

Use factoring to find the base of the triangle.

Height: 12ft
Base: 6 ft

Practice makes perfect

We know that a triangle has a height that is 6 feet longer than its base. Let x be the base of the triangle. Then, its height is x+6.

This triangle has an area of 36 square feet. Let's use the formula for the area of a triangle to write an equation. A=1/2bh ⇒ 36 = 1/2 x( x+6) We want to find x. Let's first rewrite the equation.

36=1/2x(x+6)
MultEqn

LHS * 2=RHS* 2

72=x(x+6)
Distr

Distribute x

72=x^2+6x
SubEqn

LHS-72=RHS-72

0=x^2+6x-72
RearrangeEqn

Rearrange equation

x^2+6x-72=0

Now, we will use factoring.

x^2+6x-72=0
WriteDiff

Write as a difference

x^2+12x-6x-72=0
â–¼
Factor out x & (- 6)
FactorOut

Factor out x

x(x+12)-6x-72=0
FactorOut

Factor out - 6

x(x+12)-6(x+12)=0
FactorOut

Factor out (x+12)

(x-6)(x+12)=0

To solve this equation, we will apply the Zero Product Property.

(x-6)(x+12)=0
ZeroProdProp

Use the Zero Product Property

lcx-6=0 & (I) x+12=0 & (II)
AddEqn

(I): LHS+6=RHS+6

lx=6 x+12=0
SubEqn

(II): LHS-12=RHS-12

lx_1=6 x_2=- 12

Since dimensions cannot be negative, the base x is 6 feet and the height is 12 feet.

Checking Our Answer

 Checking Our Answer
Let's find the area of a triangle with a base of 6ft and a height of 12ft. A= 1/26(12) =36 It is 36ft^2, as it is given in the exercise.
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arrow_right Exercises p.49-51
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Exercises 2 (Page 49)
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