Question

the length of side forming right angle of a right angle are 5x cm and(3x-1)cm .if the area of the triangle is 60cm²,find it's hypotenuse

Answer 1

so as we know that the area of the Triangle = 1/2*base*height = 1/2*5x*(3x-1) = 60 =>5x*(3x-1) = 60*2=120=>15x^2-5x-120=0 =>3x^2-x-24=0 =>3x^2-9x+8x-24=0 =>3x(x-3)+8(x-3)=0 =>(x-3)(3x+8)=0 =>x=3..and x=-8/3...so hypotenuse^2=(5*3)^2+(3*3-1)^2 =>225+64=289..so hypotenuse=
√289 cm = 17 cm

Answer 2

First find the value of x by using
1/2base x height= area given

Then by pythagorus theorum find the third side