Question

The perimeter of a right triangle is 30 cm. If its hypotenuse is 13 cm, then what are two sides? (3)

Answer 1

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Right angled triangle

Solve for leg

a=12cm

or

5cm

Using the formulas

P=a+b+a2+b2

c=a2+b2

There are 2 solutions fora

a=1

22P﹣P2+2Pc+c2+2c2﹣2c﹣P2+2Pc+c2=1

2·2·30·﹣302+2·30·13+132+2·132﹣2·13·﹣302+2·30·13+132=12cm

a=1

22c2﹣2P﹣P2+2Pc+c2+2c﹣P2+2Pc+c2=1

2·2·132﹣2·30·﹣302+2·30·13+132+2·13·﹣302+2·30·13+132

=5cm

Answer 2

Solution :-

The perimeter of a right angled triangle is 30cm

The hypotenuse is 13cm

Let the sides of triangle a , b and c

We know that,

Perimeter of triangle = S + S + S

Put the required values,

30 = a + b + c

30 = a + b + 13

a + b = 30 - 13

a + b = 17

a = 17 - b. ( 1 )

Now,

By using Pythagoras theorem,

c^2 = a^2 + b^2

Subsitute all the values,

( 13)^2 = ( 17 - b)^2 + b^2

[ From ( 1 ) a = 17 - b ]

169 = 289 + b^2 - 34b + b^2

[ Using identity ( a - b)^2 = a^2+b^2-2ab]

169 - 289 = 2b^2 - 34b

-120 = 2b^2 - 34b

2b^2 - 34b + 120 = 0

2 ( b^2 - 17b + 60 ) = 0

b^2 - 17b + 60 = 0

By factorization method,

b^2 - 12b - 5b + 60 = 0

b( b - 12) - 5 ( b - 12) = 0

( b - 5 ) ( b - 12 ) = 0

Here,

b = 5 and b = 12

So,

If the value of b = 5 then a = 17 - 5 = 12

If the Value of b = 12 then a = 17 - 12 = 5

Hence, The value of other two sides of triangle is 12 and 5 $.$