# Worksheet: Applications of Quadratic Equations

In this worksheet, we will practice solving word problems by forming and solving quadratic equations.

**Q6: **

Which of the following exceeds its multiplicative inverse by ?

- A or 5
- B or
- C or
- D6 or
- E or

**Q7: **

Given that nine times the square of is 25, what are the possible values of ?

- A or
- B5 or
- C
- D or

**Q8: **

Determine the positive number whose square exceeds twice its value by 15.

**Q9: **

Find the positive number whose square is equal to two times the number.

**Q10: **

The difference between the square of Danielβs age now and 5 times his age 2 years ago is 160. How old is Daniel now?

**Q11: **

When twice the square of a number is added to 1, the result is 99. What is the number?

- A7 or
- B10 or
- C10
- D98

**Q12: **

Find two numbers with a sum of 10 and a product of 9.

- A8, 2
- B6, 5
- C1, 9
- D5, 5
- E3, 7

**Q13: **

Find the positive number which is 66 less than twice its square.

**Q14: **

Given that , , and , find .

**Q15: **

An interior designer bought a rectangular rug for a room. The roomβs floor is a rectangle of width 8 m and length 15 m, and the rug is placed centrally, leaving a border of constant width around it. If the rug covers half of the floorβs area, how wide is the border?

**Q16: **

Point lies between points and . If , , and , find the length of .

**Q17: **

The sum of the squares of two positive real numbers is 542. Given that one of them is 18, find the value of the other one.

- A
- B or
- C
- D
- E or

**Q18: **

The height of a right triangle is 2 m less
than three times its base length. Its area is 4 m^{2}.
Write an equation that can be used to find the base length of the triangle, , in meters.

- A
- B
- C
- D
- E

**Q19: **

Mr. William tells his math class, βWhen I subtract a positive number from the square of the number, the result is the same as when I triple the sum of the number and four.β

What was Mr. Williamβs number?

**Q20: **

Consider the following figure.

Write an equation for , the area of the rectangle, in terms of . Simplify your equation so that there are no brackets.

- A
- B
- C
- D
- E

If the value of is 9, what is the area of the rectangle?

If the area of the rectangle is 32, what is the value of ?

**Q21: **

What is the perimeter of a rectangle whose length is 7 cm
more than its width and whose area is 78 cm^{2}?

- A18 cm
- B19 cm
- C24 cm
- D17 cm
- E38 cm

**Q22: **

The diagram shows a rectangular prism, where the area of its net is 580. Find the value of .

**Q23: **

A rectangle has a perimeter of 18, where its sides have dimensions and . Find the ratio of its longer side to its shorter one.

- A
- B
- C
- D
- E

**Q24: **

A right-angled triangle has area 150 cm^{2}. If the lengths of its perpendicular sides are cm and cm, what is its perimeter?

**Q25: **

The diagram shows a trapezoid and a rectangle.

Write an expression for the area of the rectangle.

- A
- B
- C
- D
- E

Write an expression for the area of the trapezoid.

- A
- B
- C
- D
- E

If the trapezoid and the rectangle have the same area, find the value of using a suitable equation