Question

the length of sides of forming a right triangle 5xcm and 3x-1 cm if the area of the triangle is 60 cm sq find its hypotenuse

Answer 1

ar of Δ=60
⇒1/2×(5x)×(3x-1)=60
⇒5(3x²-x)=120
⇒3x²-x=24
⇒3x²-x-24=0
⇒3x²-9x+8x-24=0
⇒3x(x-3)+8(x-3)=0
⇒(3x+8)(x-3)=0
∵x is always +ve          (length)
∴x=3
by using pythagoras theorem,
⇒hyp²=(5x)²+(3x-1)²
⇒hyp²=25x²+9x²-6x+1
⇒hyp²= 34x²-6x+1
⇒hyp²=34(3)²-6(3)+1
⇒hyp²=306-18+1
⇒hyp²=288+1
⇒hyp²=289
⇒hyp=√289
⇒hyp=17 cm
∴hypotenuse=17 cm