Question

Perimeter of triangle is 144m. If one side is 12 m greater than the base and the other side is 12 m smaller than the base,find the base of the triangle.

Answer 1

$\huge\mathbb{\underline{SOLUTION:-}}$

$\bold{Given}\begin{cases}\sf{perimeter\:of\: traingle}\\ \sf{\implies 144m}\end{cases}$

• Let the base be x

• other side is x+12

• 3rd side=x-12

$\tt\underline{\purple{perimeter\:of\: triangle=sum\:of\:all\:sides}}$

$\bold{Given}\begin{cases}\sf{perimeter\:of\: traingle=144}\\ \sf{Base=x}\\ \sf{2 \:sides =(x+12)\:and\:(x-12)}\end{cases}$

$\sf Perimeter=sum\:of\:all\:sides\\ \\ \sf\implies 144=x+x+12+x-12\\ \\ \sf\implies 144=3x+\cancel{12}-\cancel{12}\\ \\ \sf\implies 144=3x\\ \\ \sf\implies \cancel{\frac{144}{3}}=x\\ \\ \sf\implies x=48$

• The value of x =48

●So the base of triangle is 48m

$\boxed{\sf{Base=48m}}$

and one side is 12m greater than base

so side

$\sf\implies 12+48\\ \\ \sf\implies 1\: side=60m$

• Other side is smaller by 12 m

$\sf\implies 48-12\\ \\ \sf\implies other\:side=36m$

$\boxed{\purple{\sf{3\:sides\:of\: triangle=48m\:60m\:36m}}}$

$\large\bold{\red{Verification:-}}$

$\sf perimeter=sum\:of\:all\:sides$

$\bold{Side\:of\: \triangle}\begin{cases}\sf{base=48}\\ \sf{two\:sides=36\:and\:60}\end{cases}$

$\sf perimeter=a+b+c\\ \\ \sf\implies where\:a\:,b\:,c\:are\:sides\\ \\ \sf\leadsto 144=36+48+60\\ \\ \sf\leadsto 144m=144m$

L.H.S=R.H.S

$\underline{\underline{\sf{Base \:of\: triangle=48cm}}}$

#BAL

#answerwithquality