Lesson Worksheet: Applications of Quadratic Equations Mathematics • 9th Grade

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


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


What is the perimeter of a rectangle whose length is 7 cm more than its width and whose area is 78 cm2?


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


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


The difference between the lengths of the diagonals of a rhombus is 5 cm. Given that its perimeter is 304 cm, find the lengths of the diagonals to the nearest cm.

  • A115 cm, 100 cm
  • B219 cm, 209 cm
  • C204 cm, 204 cm
  • D110 cm, 105 cm


Point 𝐾 lies between points 𝐽 and 𝐿. If 𝐽𝐾=𝑥+8𝑥, 𝐾𝐿=3𝑥2, and 𝐽𝐿=40, find the length of 𝐽𝐾.


The diagram shows a trapezoid and a rectangle.

Write an expression for the area of the rectangle.

  • A(2𝑥+1)(𝑥9)
  • B2(2𝑥+1)(𝑥9)
  • C(2𝑥1)(𝑥+8)
  • D(2𝑥+3)(𝑥7)
  • E2((2𝑥+1)+(𝑥9))

Write an expression for the area of the trapezoid.

  • A(𝑥7)(𝑥+3)
  • B(𝑥+6)(𝑥7)
  • C(𝑥8)(𝑥+7)
  • D(𝑥3)(𝑥6)
  • E(𝑥+5)(2𝑥3)

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


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.

  • A866
  • B866 or 866
  • C2131
  • D218
  • E218 or 218


A right triangle has sides of lengths 𝑛 cm, 3(𝑛+1) cm, and (3𝑛+4) cm. Find the length of its shortest side.

Hint: first, decide which side is the hypotenuse.


If the area of the given figure is 138 cm2, what is the value of 𝑥?

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