Question

11. The sides of a right-angled triangle are in the ratio x: (x - 1) : (x - 18). What is the perimeter of the triangle? - (a) 28 units (b) 42 units (c) 56 units (d) 84 units​

Answer 1

formula:

using Pythagoras theorem;

(diagonal)^2=(side1)^2+(side2)^2

given:

ratio of sides of triangles are x:(x-1):(x-18)

solution:

let the sides of the traingle be ax,a(x-1),a(x-18) respectively

using the Pythagoras theorem,

$(ax) ^{2} = (a(x - 1)) ^{2} + (a(x - 18)) { }^{2}$

$x { }^{2} = x {}^{2} + 1 - 2x + x {}^{2} + 324 - 36x$

$x {}^{2} - 38x + 325 = 0$

finding roots of x,

x=25,-13

negative values of x can't be considered

the sides of the triangles are:

x=25

x-1=24

x-18=7

perimeter=25+24+7=56 units

option (c)56 units