793 views

### For a cuboid, the longest side is two units more than the shortest side, and the middle length side is one unit longer than the shortest side. The total surface area of the cuboid is 52 units². (a) Construct an equation to calculate the surface area.

First label all the sides with letters:

longest side = a

middle length side = b

shortest side = c

Now convert the question into equation form:

"the longest side is two units more than the shortest side" becomes, a = 2 + c (1)

"middle length side is one unit longer than the shortest side" becomes, b = 1 + c (2)

"The total surface area of the cuboid is 52 units² " becomes, 2*a*b + 2*a*c + 2*b*c = 52 (3)

Substitute expressions (1) and (2) into (3) to get

2(2+c)(1+c) + 2c(2+c) + 2c(1+c) = 52

Expand out the brackets:

2(2+3c+c^2) + 4c + 2c^2 + 2c + 2c^2 = 52

which becomes:

4 + 6c + 2c^2 + 6c + 4c^2 = 52

collect all the terms together:

6c^2 + 12c - 48 = 0

Divide by 6 to simplify equation:

c^2 + 2c - 8 = 0

factorise this equation into brackets to find c, by finding two numbers that multiply together to make -8, and add together to make 2... i.e. 4 and -2,

(c + 4)(c-2) = 0

Therefore, c = -4, or c=2. Since c must be positive (a negative side length would make no physical sense) c must be 2. We can then subsitute this back into (1) and (2) to find values for a and b,

a = 4

b = 3

and then double check that the surface area is 52.

1 year ago

Answered by Eden, a GCSE Maths tutor with MyTutor

## Still stuck? Get one-to-one help from a personally interviewed subject specialist

#### 655 SUBJECT SPECIALISTS

£36 /hr

Degree: Economics with French (Bachelors) - Bristol University

Subjects offered:Maths, Spanish+ 2 more

Maths
Spanish
French
Economics

“Private tutor of Economics, Maths and French with six years of experience. I am passionate about teaching!”

£22 /hr

Degree: Biological Sciences with a Year in Industry/Research (Bachelors) - Imperial College London University

Subjects offered:Maths, Chemistry+ 1 more

Maths
Chemistry
Biology

£22 /hr

Degree: Physics with Theoretical Physics (Masters) - Kings, London University

Subjects offered:Maths, Spanish+ 1 more

Maths
Spanish
Physics

“I am a Physics with Theoretical Physics student at King´s College London. And if there is something that I love even more than Physics and Science is learning. I love it so much that I decided to leave my country, leaving there my fam...”

Currently unavailable: for regular students

Degree: Engineering Science (Masters) - Oxford, Somerville College University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“Hi, I'm Eden, a fourth year engineering student at the University of Oxford. When I was taking my GCSEs my Maths teacher showed me how maths is the language we use to describe our reality, and ever since then I've been impassioned to ...”

### You may also like...

#### Posts by Eden

For a cuboid, the longest side is two units more than the shortest side, and the middle length side is one unit longer than the shortest side. The total surface area of the cuboid is 52 units². (a) Construct an equation to calculate the surface area.

The roots of the equation z^3 + 2z^2 +3z - 4 = 0, are a, b and c . Show that a^2 + b^2 +c^2 = -2

What is the natural logarithm?

#### Other GCSE Maths questions

If I buy a dress at 30% off the original price and I pay £40. How much was the dress originally?

Solve the following simultaneous equations: x^2-y^2=9, x - y = 1

work out the value of 4a + 2b when a = 4 and b = 3

Solve: 3(x - 2) = 21

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this.