Question

the sides of a right angle triangle containing the right angle are 4xcm and (2x-1)cm.If area of the triangle is 30cm square find length of its side​

Answer 1

We have,

height =4x cm

base=(2x-1) cm

Area of a triangle=30 cm²

Area of a triangle=(1/2)×base× height

30=(1/2)×4x × (2x-1)

30=2x(2x-1)

4x²-2x-30=0

2x²-x-15=0

2x²-6x+5x-15=0

2x(x-3)+5(x-3)=0

(2x+5)+(x-3)=0

Either 2x+5 =0

This gives x=-5/2

or x-3=0

This gives x=3

Since length can't be in negative, so we choose the value as x=3.

Thus, height =4x= 4×3 =12 cm

and breadth = (2x-1) = 2×3-1=5 cm