Doubt by Jugal
Solution :
Area of isosceles triangle = 12 cm²
Length of each equal sides (a) = 5 cm
Base of the isosceles triangle (b) = ?
12 = (b/4)√[4(5)²-b²]
SBS
(12)²=(b²/16)[100-b²]
144×16=b²(100-b²)
2304=100b²-b⁴
b⁴-100b²+2304=0
(b²)²-100b²+2304=0
Let b²=x
x²-100x+2304=0
x²-(64+36)x+2304=0
x²-64x-36x+2304=0
x(x-64)-36(x-64)=0
(x-36)(x-64)=0
x-36=0
x=36
b²=36
b=±√36
OR
(x-64)=0
x=64
b²=64
b=±√64
b=±8
but base can't be -ve
so b=8 cm
Hence, the base of the isosceles triangle is either 6 cm or 8 cm.
Length of each equal sides (a) = 5 cm
Base of the isosceles triangle (b) = ?
12 = (b/4)√[4(5)²-b²]
SBS
(12)²=(b²/16)[100-b²]
144×16=b²(100-b²)
2304=100b²-b⁴
b⁴-100b²+2304=0
(b²)²-100b²+2304=0
Let b²=x
x²-100x+2304=0
x²-(64+36)x+2304=0
x²-64x-36x+2304=0
x(x-64)-36(x-64)=0
(x-36)(x-64)=0
x-36=0
x=36
b²=36
b=±√36
b=±6
but base can't be -ve
so b=6 cm
but base can't be -ve
so b=6 cm
OR
(x-64)=0
x=64
b²=64
b=±√64
b=±8
but base can't be -ve
so b=8 cm
Hence, the base of the isosceles triangle is either 6 cm or 8 cm.