Question

7. 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.

A. leg = 15 feet, leg = 29 feet
B. leg = 5 feet, leg = 19 feet
C. leg = 10 feet, leg = 24 feet
D. leg = 11 feet, leg = 25 feet

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

A. 2
B. 3
C. 0
D. 1

15. 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?

A. length = 20 meters, width = 4 meters
B. length = 10 meters, width = 8 meters
C. length = 14 meters, width = 12 meters
D. length = 8 meters, width = 6 meters

19. 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?

A. length = 20 inches, width = 17 inches
B. length = 17 inches, width = 14 inches
C. length = 34 inches, width = 10 inches
D. length = 10 inches, width = 7 inches

Answer 1

7. 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 2

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

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.