The area of a rectangle is 8cm^2. It has a length of (3x+1)cm and a width of (2x+5)cm. Work out the value of x.

We know that the equation of the area of a rectangle is width times by length. Therefore:

8=(3x+1)(2x+5)

If we multiply out the brackets we get:

8=(6x2+2x+15x+5), thus, 8=6x2+17x+5, and therefore, 0=6x2+17x-3

One technique that I found useful to find the value of x when the coefficient of x2 is greater than one is to split the coefficient of x. Therefore we must find 2 numbers that when multiplied equal (-18) and add to 17. The answer to this is 18 and (-1).

Thus we get, 0=6x2+18x-x-3. We can then factorise this equation to 0=6x(x+3)-1(x+3), and then 0=(6x-1)(x+3). This means that we get 2 answers to this quadratic - when 6x-1=0 and x+3=0.

Thus x=1/6 and -3. As x cannot be negetive, the answer is 1/6.

Answered by Oliver C. Maths tutor

11606 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Find the value of X when 3x^2 + 6x + 3 = 0


Solve the simultaneous equations “x^2+y^2=4” and “x=2-y”. What does this tell us about the circle centred on the origin, with radius 2, and the straight line with y-intercept 2 and gradient -1?


Work out 64^1/2


Solve the following pair of simultaneous equations; 10x+4y=15, 2x+y=7


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences