(b) The perimeter of a right angled triangle is 30cm. If the hypotenuse is lem
more than the perpendicular and Seni more than the base, find the sides of
the right angled triangle.
Answers
Request:
can u first pl explain what are 1em and Seni
Answer:
Perimeter of a right angled triangle =30cms.
We know, Perimeter of a right angled triangle =a+b+c and a
2
+b
2
=c
2
where a,b are two sides and c is the hypotenuse of a triangle.
Also, it is given c=13cms.
∴ a+b+13=30 and a
2
+b
2
=13
2
⟹ a+b=17 ........ (1) and a
2
+b
2
=169 ............ (2)
From (1), a=17−b
Substitute value of a in equation (2) we get,
(17−b)
2
+b
2
=169
⟹ 289−34b+b
2
+b
2
=169
⟹ 2b
2
−34b+120=0
⟹ b
2
−17b+60=0
⟹ b
2
−12b−5b+60=0 ...... factorized above equation
⟹ b(b−12)−5(b−12)=0
⟹ (b−12)(b−5)=0
∴ b=12 or b=5
If b=12 then a=17−12=5
If b=5 then a=17−5=12.
Hence the length of other two sides are 12,5.
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