SOLUTION: A banner is in the shape of a right triangle of area 63 in^2. The height of the banner is 4 inches less than twice the width of the banner. Find the height and the width of the ban

Question 941039: A banner is in the shape of a right triangle of area 63 in^2. The height of the banner is 4 inches less than twice the width of the banner. Find the height and the width of the banner.
Found 3 solutions by Fombitz, macston, MathTherapy:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!

Substituting,

Only the positive solution makes sense here.

Answer by macston(5194)   (Show Source): You can put this solution on YOUR website!
W=width of banner; H=height of banner=2W-4; A=Area of banner=1/2WH=63 sq in
Substitute for H first equation)in the area equation and solve for W:
1/2WH=63 sq in
1/2W(2W-4)=63 sq in

Subtract 63in^2 from each side

(((W^2-2W-63in^2=0}}}

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=256 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 9, -7. Here's your graph:

So W=9,-7
First Let's consider 9
When W=9, H=2W-4=2(9)-4=14
ANSWER Width is 9 in and Height is 14 in, a tall narrow right triangle pointing upward and to the right.
CHECK:
Area=1/2WH=63 in sq
Area=1/2(9in)(14in)=63 in sq
Area=1/2(126in sq)=63 in sq
Area=63 in sq=63 in sq, Check
Next, let's consider -7. At first this seems an unlikely width, but if we consider on an X,Y co-ordinate plane right is the positive direction, it means this banner points left. So solving for height:
H=2W-4=2(-7)-4=-14-4=-18, again negative, so pointing down
So we have a banner of Width=7 in and Height=18 in pointing left and downward
CHECK:
Area=1/2WH=1/2(-7in)(-18 in)=63 in sq
Area=1/2(126 in sq)=63in sq
Area= 63 in sq=63 in sq Check
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

A banner is in the shape of a right triangle of area 63 in^2. The height of the banner is 4 inches less than twice the width of the banner. Find the height and the width of the banner.

Let base of banner be B
Then height = 2B - 4
Since area = 63 ⁱⁿ, then it can be said that:

(B - 9)(B + 7) = 0
B, or base = inches
Height: 2(9) - 4, or 18 - 4, or inches
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