The base of an isoceles of triangle measure 24cm area of triangle 192cm square. Find the perimeter

The base of an isoceles of triangle measure 24cm area of triangle 192c

1.	The base of an isoceles of triangle measure 24cm area of triangle 192cm square. Find the perimeter
Answer» Here, base, b = 24 cm, and let each equal side be a cm. Then,area =\xa0{tex}\\frac { 1 } { 4 } b \\sqrt { 4 a ^ { 2 } - b ^ { 2 } } \\text { sq units } = \\frac { 1 } { 4 } \\times 24 \\times \\sqrt { 4 a ^ { 2 } - 576 } \\mathrm { cm } ^ { 2 }{/tex}={tex}12 \\times \\sqrt { a ^ { 2 } - 144 } \\mathrm { cm } ^ { 2 }{/tex}But, area = 192 cm2 [given].{tex}\\therefore \\quad 12 \\times \\sqrt { a ^ { 2 } - 144 } = 192 \\Rightarrow \\sqrt { a ^ { 2 } - 144 } = 16{/tex}{tex}\\Rightarrow a ^ { 2 } - 144 = 256 \\Rightarrow a ^ { 2 } = 400 \\Rightarrow a = 20{/tex}{tex}\\therefore\\quad {/tex}perimeter of the triangle = (2a + b) cm= (2 {tex}\\times{/tex}\xa020 + 24) cm = 64 cm. 24cm one side and anotjer two are equal and will be x 192=1/2(base)(hight)192=1/2×24(x)192=12X192/12=x16=xSo, two equal sides are of 16cm.Perimeter =24+16+16P=54