Question

the length of the sides of a angled triangle are 5 xcm and (3 x+1) cm ,if the area of the triangle is 60sqcm ,find the hypotenuse​

Answer 1

Answer:

Area of a right angled triangle

=

2

1

×b×h

⇒60=

2

1

×(5x)×(3x−1)

⇒24=x(3x−1)

⇒3x

2

−x−24=0

⇒3x

2

−9x+8x−24=0

⇒3x(x−3)+8(x−3)=0

∴x=−

3

8

, 3

For x=3, AB=3(3)−1=9−1=8

BC=5×3=15

AB

2

+BC

2

=AC

2

⇒AC

2

=8

2

+15

2

=64+225=289

∴AC=17 units(cm)

∴ perimeter =AB+BC+CA

=8+15+17=40cm.