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  1. The hypotenuse of a right triangle is 26 feet long. One leg of the triangle is 14 feet longer than the other leg. Find the lengths of the legs of the triangle.
Aleg = 15 feet, leg = 29 feet
Bleg = 5 feet, leg = 19 feet
Cleg = 10 feet, leg = 24 feet
Dleg = 11 feet, leg = 25 feet

  1. Use the discriminant to determine how many real number solutions exist for the quadratic equation –4j2 + 3j – 28 = 0.

A2
B3
C0
D1

  1. The length of a rectangle is 2 meters more than its width. The area of the rectangle is 80 square meters. What is the length and width of the rectangle?

Alength = 20 meters, width = 4 meters
Blength = 10 meters, width = 8 meters
Clength = 14 meters, width = 12 meters
Dlength = 8 meters, width = 6 meters

  1. The width of a rectangle is 3 inches less than its length. The area of the rectangle is 340 square inches. What are the length and width of the rectangle?

Alength = 20 inches, width = 17 inches
Blength = 17 inches, width = 14 inches
Clength = 34 inches, width = 10 inches
Dlength = 10 inches, width = 7 inches

Verified Answer :

tnovack30tynova163
  1. C. leg = 10 feet, leg = 24 feet 
    13.     A. 2
    15.     D. length = 8 meters, width = 6 meters
    19.     A. length = 20 inches, width = 17 inches

Answer:

7. C. leg = 10 feet, leg = 24 feet

13. A. 2

15. B. length = 10 meters, width = 8 meters

19. A. length = 20 inches, width = 17 inches

Step-by-step explanation:

7. By the pythagoras theorem we know that,

Let one Leg be x

then other leg will be x + 14. Hence,

(Hypotenuse)² = (Base)² + (Perpendicular)²

(26)² = (x)² + (x + 14)²

676 = x² + x² + 28x + 196

480 = 2x² + 28x

x = 10, -24

So, lengths of legs is 10 feet and 24 feet.

13. Discriminant is calculated by formula:

     D = b² - 4ac

where a is coefficient of x²

           b is coefficient of x

          and c is intercept

Now, calculating Discriminant:

        D = 9 - 4×(-4)×(-28) = -439 < 0

Hence, equation has no real solutions.

15. Let width be x.

then, Length = 2 + x.

Area of rectangle = Length × Width

                     80    = (2 + x) × x

x² + 2x = 80

x = -10, 8

Hence, width = 8 meters and length = 10 meters

19. Let Length be x.

then, Width = x-3.

Area of rectangle = Length × Width

340 = x × (x-3)

x= -17 , 20

Hence, width = 17 meters and length = 20 meters.

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