Question

perimeter of a. triangle 49cm one side is 7cm more than second side and 5cm less than the third side find length of three side​

Answer 1

EXPLANATION.

Perimeter of the triangle = 49 CM.

one side is 7 CM more than second side.

5 CM is less than the third side.

To find length of three sides.

As we know that,

perimeter of triangle = a + b + c

=> 49 = a + b + c

one side is 7 CM more than second side.

=> a = b + 7 => b = a - 7 ..... (1)

5 CM is less than the third side.

=> a = c - 5 => c = a + 5 ..... (2)

put the value in equation we get,

=> 49 = a + ( a - 7 ) + ( a + 5 )

=> 49 = a + a - 7 + a + 5

=> 49 = 3a - 2

=> 51 = 3a

=> a = 17

Therefore,

=> a = 17 CM.

=> b = a - 7 = 17 - 7 = 10 CM.

=> c = a + 5 = 17 + 5 = 22 CM.

Answer 2

Answer:

• Let the First side of triangle be x

• Second side be x + 7

• Third side be x + 5

❍ Given : Perimeter of triangle is 49cm.

• As we know that, the Perimeter of triangle is equal to the sum of all three sides :]

__________________

☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$:\implies \sf x + (x - 7) + (x + 5) = 49$

.

$:\implies \sf x + x - 7 + x + 5= 49$

$:\implies \sf 3x - 2= 49$

$:\implies \sf 3x = 49 + 2$

$:\implies \sf 3x = 51$

$:\implies \sf x = \frac{51}{3}$

$:\implies \underline{ \boxed{\sf x = 17 \: cm}} \: \: \: \bigg \lgroup \bf First \: side \: of \: \Delta \bigg \rgroup$

$\bigstar\:\:\underline{\bf Therefore, \sf Length \: of \: three \: sides \: of \: \Delta \: are: }$

$\bullet\:\:\textsf{First side = \textbf{17 cm}}$

$\bullet\:\:\textsf{Second side = x - 7 = 17 - 7 = \textbf{10 cm}}$

$\bullet\:\:\textsf{Third side = x + 5 = 17 + 5 = \textbf{22 cm}}$