698 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

#### 533 SUBJECT SPECIALISTS

£22 /hr

Ayusha A.

Degree: BEng electrical and electronics engineering (Bachelors) - Newcastle University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“About me: I am a final year Electrical and Electronic Engineering student at Newcastle University. I took Mathematics, Further Mathematics, Chemistry and Physics as my A-level subjects. I did peer mentoring in university and also have...”

£20 /hr

Xanthe W.

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

Hinsum W.

Degree: Medicine (Bachelors) - Edinburgh University

Subjects offered:Maths, Chemistry+ 3 more

Maths
Chemistry
Biology
-Personal Statements-
-Medical School Preparation-

“Hi, I'm a first year medic at Edinburgh. I've had 7 years' worth of experience teaching children Maths and English and have mentored lower school peers, so I'm bound to have an approach that will suit your learning style!”

Eden H.

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

What are the differences between arithmetic and geometric sequences?

Solve 5x - 7 = 3x + 2, to find the value of x

Bag A contains £7.20 in 20p coins. Bag B contains only 5p coins. The number of coins in bag B is three-quarters of the number of coins in bag A. How much money is in bag B? (in £s)

Where does the quadratic equation come from?

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