Question

The length of the sides forming right angle of a right angled triangle are 5x cm and (3x-1)cm.if the area of the triangle is 60cm2,find its hypotenuse??

Answer 1

Area =1/2(5x)(3x-1)=60

=>3x^2-x-24=0

=>3x^2 -9x+8x-24=0

=>x=3

Then ,sides are =5(3)=15 and 3(3)-1=8

Hypotenuse=√(225+64)=17cm

Hope it helps

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Area of triangle = 1/2 × base × height

= 1/2 × 5x × (3x - 1)

According to the Question,

15x² - 5x = 120

⇒ 3x² - x - 24 = 0

⇒ 3x² - 9 + 8x - 24 = 0

⇒ 3x(x - 3) + 8(x - 3) = 0

⇒ (x - 3) (3x + 8) =

⇒ x = 3, - 8/3 (As x can't be negative)

⇒ x = 3

AB = 5 × 3 = 15 cm

BC = 3x - 1 = 9 - 1 = 8 cm

AC = √15² + 8²

= √225 + 64

= √289

= 17 cm

Hence, the hypotenuse is 17 cm.