a right-angled triangle has base 2x + 1, height h and hypotenuse 3x. show that h^2 = 5x^2 - 4x - 1

initially, explain Pythagorean's Theory --> a^2 + b^2 = c^2.explain c is the hypotenuse, a and b can be either base or height.using a as base and b as height, a = 2x+1. b = h. c = 3xsubstitute into formula:(2x+1)^2 + h^2 = 9x^2expanding brackets (using FOIL):4x^2 + 4x + 1 + h^2 = 9x^2rearranging so h^2 is the subject:h^2 = 5x^2 - 4x - 1

MA
Answered by Mohammad A. Maths tutor

3018 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Solve the simultaneous equations;5x +y = 21 and x-3y=9


The first floor of an ancient japanese tower has 150 steps. Each floor above has 5 fewer floors than the previous. So, the second floor has 145 steps, the third 140 etc. How many floors does the tower have if the final floor has 30 steps leading to it.


Solve the simultaneous equations 7x - 2y = 22 and 5x + 3y = 29


Expand and simplify (x+4)(x-5).


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