SOLUTION: ABC is a triangle with sides a, b, and c, as shown in the diagram. If angle C = 90 degrees, c = 4, and a + b = the square root of 18, then the area of the triangle is... A)1/2 B)1

Algebra.Com
Question 665289: ABC is a triangle with sides a, b, and c, as shown in the diagram. If angle C = 90 degrees, c = 4, and a + b = the square root of 18, then the area of the triangle is... A)1/2 B)1 C)2 D)4 E)18
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
ABC is a triangle with sides a, b, and c, as shown in the diagram. If angle C = 90 degrees, c = 4, and a + b = the square root of 18, then the area of the triangle is... A)1/2 B)1 C)2 D)4 E)18 
Since a + b = Ö18, b = Ö18 - a. 



The area is A = ab = a(Ö18 - a)

By the Pythagorean theorem:

a² + b² = c²

a² + (Ö18 - a)² = 4²

a² + 18 - 2aÖ18 + a² = 16

2a² - 2aÖ18 = -2

Divide through by 2

a² - aÖ18 = -1

Multiply through by -1

-a² + aÖ18 = +1

aÖ18 - a² = 1

Factor out a on the left:

a(a - Ö18) = 1

Notice that the area above is A = a(Ö18 - a), which just
happens to be the left side multiplied by . So let's
multiplty both sides of that equation through by :

a(a - Ö18) = ·1

So Area = a(a - Ö18) = 

Answer:  

Edwin
RELATED QUESTIONS

In the right triangle ABC, AC= 12, angle B= 30 degrees, Angle C= 90 degrees, and Angle A= (answered by Alan3354)
if in triangle ABC, the measure of angle B is greater than 90 degrees, and AB= BC, what... (answered by MathLover1)
In triangle ABC, if angle A = 51 degrees and angle B = 73 degrees, what is the measure of (answered by Alan3354)
In triangle ABC, angle A is twice as big as angle B, and angle C is 90°. Find the... (answered by Stitch)
in triangle ABC with right angle at C angle B=30 and side a = 4 square root... (answered by Alan3354)
in a acute angle triangle ABC if SIN (B+C-A) = (SQUARE ROOT 3) /2 and TAN... (answered by ikleyn)
In a triangle ABC, angle B= 55° and angle C=65°. Is the triangle ABC... (answered by Alan3354)
Draw triangle ABC. Label angle A 30 degrees, angle B 70 degrees and angle C 80 degrees.... (answered by mananth)
Solve Triangle ABC. A=90, b=4, c=7. i figured out that the hypotenuse (leg a) is the... (answered by stanbon)