Question

find the area of a right triangle whose sides containing the right angle are 18 cm and 16 cm

Answer 1

${\huge{\bold{\underline{Answer:-}}}}$

Area of a right angled triangle

=21×b×h

⇒60=21×(5x)×(3x−1)

⇒24=x(3x−1)

⇒3x2−x−24=0

⇒3x2−9x+8x−24=0

⇒3x(x−3)+8(x−3)=0

∴x=−38, 3

For x=3, AB=3(3)−1=9−1=8

BC=5×3=15

AB2+BC2=AC2

⇒AC2=82+152=64+225=289

∴AC=17 units(cm)

∴ perimeter =AB+BC+CA

=8+15+17=40cm.

Answer 2

$\large \tt \blue {answer}$

Area of a right angled triangle

=21×b×h

⇒60=21×(5x)×(3x−1)

⇒24=x(3x−1)

⇒3x2−x−24=0

⇒3x2−9x+8x−24=0

⇒3x(x−3)+8(x−3)=0

∴x=−38, 3

For x=3, AB=3(3)−1=9−1=8

BC=5×3=15

AB2+BC2=AC2

⇒AC2=82+152=64+225=289

∴AC=17 units(cm)

∴ perimeter =AB+BC+CA

=8+15+17=40cm.