sides of right triangle containing right angle and 5x cm and 3x-1cm if its area is 60cm2 then find the length
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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.
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