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.
