A cuboid has length x cm. The width of the cuboid is 4 cm less than its length. The height of the cuboid is half of its length. The surface area of the cuboid is 90 cm^2 . Show that 2x^2 − 6x − 45 = 0

Take each side of the cuboid as an algebraic expression and multiply each by 2 to account for both sides of the shape. For example, (x)(x-4), which could be expanded to x2 -4x, and then multiplied by 2 to reach 2x2 -8x. Do the same for the other two expressions and then find the sum of all the sides together.(2)(x)(x/2) = x2. (2)(x-4)(x/2) = x2-4x. So, 2x2-8x +x2+x2-4x = 90 (90 here is the surface area of the cuboid we saw in the question). By simplifying this equation we reach 4x2-12x-90 = 0. Divide by 2, and we reach 2x2-6x-45 =0

TM
Answered by Tom M. Maths tutor

11171 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Factorise x 2 − x − 12


Solve the following system of simultaneous equations: y=x^2 - 5x + 4 ; x+2y=19


A bag contains 10 apples. Three of the apples are green and seven of the apples are red. If an apple is pulled from the bag at random, what is the probability that the apple will be green?


y is inversely proportional to d2 when d = 10, y = 4 d is directly proportional to x2 when x = 2, d = 24 Find a formula for y in terms of x. Give your answer in its simplest form.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning