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Answer:
\huge{\sf{Question}}Question
Two sides of a triangle are 5 and 7 cm longer than the third side. If the perimeter is 21cm, find the length of each side ?
\huge{\sf{Given:-}}Given:−
Let the third side be x
Then,
Length of first side = (x+5)cm
Length of second side = (x+7)cm
Length of third side = x cm
Perimeter = 21cm
\huge{\sf{Solution:-}}Solution:−
Perimeter of triangle = Sum of their sides
\longrightarrow⟶ \sf{(x+5+x+7+x)cm= 21cm}(x+5+x+7+x)cm=21cm
\longrightarrow⟶ \sf{(3x+12)cm = 21cm}(3x+12)cm=21cm
\longrightarrow⟶ \sf{3x=(21-12)cm}3x=(21−12)cm
\longrightarrow⟶ \sf{3x=9}3x=9
\longrightarrow⟶ \sf{x= \frac{9}{3}}x=
3
9
\longrightarrow⟶ \sf{x=3}x=3
_______________________________
\sf{\red{Therefore,the\: sides\:are:-}}Therefore,thesidesare:−
First side = (3+5)=8cm
Second side = (3+7)=10cm
Third side = 3cm
\huge{\sf{Question}}Question
Two sides of a triangle are 5 and 7 cm longer than the third side. If the perimeter is 21cm, find the length of each side ?
\huge{\sf{Given:-}}Given:−
Let the third side be x
Then,
Length of first side = (x+5)cm
Length of second side = (x+7)cm
Length of third side = x cm
Perimeter = 21cm
\huge{\sf{Solution:-}}Solution:−
Perimeter of triangle = Sum of their sides
\longrightarrow⟶ \sf{(x+5+x+7+x)cm= 21cm}(x+5+x+7+x)cm=21cm
\longrightarrow⟶ \sf{(3x+12)cm = 21cm}(3x+12)cm=21cm
\longrightarrow⟶ \sf{3x=(21-12)cm}3x=(21−12)cm
\longrightarrow⟶ \sf{3x=9}3x=9
\longrightarrow⟶ \sf{x= \frac{9}{3}}x=
3
9
\longrightarrow⟶ \sf{x=3}x=3
_______________________________
\sf{\red{Therefore,the\: sides\:are:-}}Therefore,thesidesare:−
First side = (3+5)=8cm
Second side = (3+7)=10cm
Third side = 3cm