# Sample quiz on word problems involving quadratics Main home here.

1. The hypotenuse of a right triangle measures $(2x+1)$ units, while the legs are $2x$ and $(x-1)$ units. Find the value of $x$.
A: $0$
B: $5$
C: $6$
D: $8$
2. Assuming $x> 0$, find the value of $x$ for which $(x,x+1,x+2)$ is a pythagorean triple.
A: $3$
B: $4$
C: $2$
D: $-1$
3. At any time $t$, the height $h$ of an object thrown up is given by $h=-4.9t^2+14.7t$. Find the initial height of the object.
A: $14.7$
B: $4.9$
C: $9.8$
D: $0$
4. At any time $t$, the height $h$ of an object thrown up is given by $h=-5t^2+20t$. At what time does it attain its maximum height?
A: $t=20$
B: $t=4$
C: $t=3$
D: $t=2$
5. At any time $t$ seconds, the height $h$ of an object thrown up is given by $h=-4.9t^2+19.6t+3$ (in meters). Which statement is wrong?
A: It attained its maximum at $t=2$ s
B: Its initial height is $3$ m
C: Its maximum height is $22.6$ m
D: It spent at total of $49$ s in the air.
6. The profit function for a certain item is given by $P(x)=-5x^2+300x$, where $x$ is the number of items. What is the break-even point?
A: $x=30$
B: $x=40$
C: $x=0$ or $x=60$
D: $x=0$ or $x=30$
7. The length and width of a rectangle are $(x+3)$ and $(x-2)$. Find $x$ if its area is $50$ sq. units.
A: $7$
B: $8$
C: $-7$
D: $-8$
8. A square measures $(2x-1)\times(2x-1)$. Its area is $49$ sq. units. Find the admissible value of $x$.
A: $x=8$
B: $x=7$
C: $x=4$
D: $x=-3$
9. Find the distance between the points of intersection of the quadratics $y=x^2$ and $y=-x^2+6x+8$.
A: $5\sqrt{10}$
B: $5\sqrt{3}$
C: $10\sqrt{5}$
D: $5$
10. Find two consecutive positive numbers numbers whose squares add up to $85$.
A: $5,6$
B: $6,8$
C: $7,8$
D: $6,7$