Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Please verify your account before proceeding.

In this lesson, we will learn how to solve word problems by forming and solving quadratic equations.

Q1:

The length of a rectangle is 2 cm more than its width. If its area is 80 cm^{2}, what are its length and width?

Q2:

The side length of a square is π₯ cm, and the dimensions of a rectangle are π₯ cm and 2 cm. Given that the sum of their areas is 8 cm^{2}, determine the perimeter of the square.

Q3:

A rectangular photograph measuring 6 cm by 4 cm is to be displayed in a card mount in a rectangular frame, as shown in the diagram.

Write an equation that can be used to find π₯ , the width of the mount, if its area is 64 cm^{2}.

Q4:

The length of a rectangle is 26 cm more than its width. Given that its area is 120 cm^{2}, determine its perimeter.

Q5:

The length of a rectangle is 3 cm more than double the width. The area of the rectangle is 27 cm^{2}. Write an equation that can be used to find π€ , the width of the rectangle, in centimeters.

Q6:

The sum, π , of the first π consecutive integers ( 1 + 2 + 3 + 4 + β― + π ) can be found using Starting from 1, how many consecutive integers are required to make a sum of 21?

Q7:

The height of a ball π‘ seconds after it was kicked from the ground is modeled by the function β , where β ( π‘ ) = 1 5 π‘ β 5 π‘ 2 .

For how long does the ball remain in the air?

For how long does the ball remain above a height of 10 m?

Q8:

Which of the following exceeds its multiplicative inverse by 1 1 3 0 ?

Q9:

A study was carried out to determine how many people in a small town were infected with the hepatitis C virus. An approximation for the number of infected people, π¦ , can be found using π¦ = β 0 . 5 π β 5 . 5 π + 9 3 1 ο¨ , where π is the number of years after 2006. In which year do we expect there to be no infected people?

Q10:

Find the solution set of the equation π₯ β 2 6 π₯ 9 = β 1 6 9 2 in β .

Q11:

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

Q12:

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

Q13:

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

Q14:

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

Q15:

At which values of π₯ does the graph of π¦ = 1 2 π₯ β 8 π₯ ο¨ cross the π₯ -axis?

Q16:

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

Q17:

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

Q18:

A study was carried out to investigate the number of people in a town infected by norovirus. The number of people infected, π¦ , occurring π years after the start of the study, can be found using the equation What was the value of π when there were 347 people infected?

Q19:

A rocket will be launched vertically upwards with a speed of 343 m/s.

Itβs height after launch can be found using where π is the rocketβs height in meters and π‘ is the time after launch in seconds.

What will be the height of the rocket 6 seconds after launch?

At what times will the rocket be 2β690.1 m above the ground?

Q20:

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

Q21:

Given that , , and , find .

Q22:

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?

Q23:

Two siblings are 3 years apart in age. Write an equation for π , the product of their ages, in terms of π , the age of the younger sibling.

Q24:

A formula for the normal systolic blood pressure for a man age π΄ , measured in millimeters mercury, is given as π = 0 . 0 0 6 π΄ β 0 . 0 2 π΄ + 1 2 0 2 . Find the age, to the nearest year, of a man whose normal systolic blood pressure measures 125 mmHg.

Q25:

A falling object travels a distance given by the formula π = 5 π‘ + 1 6 π‘ ο¨ ft, where π‘ is measured in seconds. How long will it take for the object to travel 74 ft?

Donβt have an account? Sign Up