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

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

Q1:

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

Q2:

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

Q3:

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

Q4:

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

Q5:

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

Q6:

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

Q7:

The diagram shows a trapezoid and a rectangle.

Write an expression for the area of the rectangle.

Write an expression for the area of the trapezoid.

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

Q8:

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

Q9:

A right triangle has sides of lengths cm, cm, and cm. Find the length of its shortest side.

Hint: first, decide which side is the hypotenuse.

Q10:

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

This lesson includes 22 additional questions and 184 additional question variations for subscribers.

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