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The area of an isosceles triangle is 12 CM square. If one of its equal sides is 5 cm,find its base. |
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Answer» Answer: 8 cm or 6 cm could be the bases Step-by-step explanation: Let half of the BASE be 'b' Hypotenuse of the triangle = 5 cm Base= b Height=h Area of a triangle= 1/2*b*h Here, the entire base is 2b THEREFORE, 1/2*2b*h=12cm^2 b*h=12 cm^2 To proceed further, Let 'h' be 12/b cm Pythagoras property a^2+b^2=c^2 b^2+(12/b)^2= 5^2 b^2+(144/b^2)=25 (b^4+144)/b^2=25 b^4+144=25b^2 b^4-25b^2+144=0 By spiting the middle term, b^4-9b^2-16b^2+144 b^2(b^2-9)-16(b^2-9) (b^2-16)(b^2-9)=0 Either,(b^2-16)=0 or (b^2-9)=0 Either b^2=16 or (b^2=9) Therefore, b can be either 4 or 3 As 2b is the base, it can be either 8 cm or 6 cm If 8 cm is the base, then 3 cm will the height. If 6 cm is the base, then 4 cm will be the height. Hope it helps you!!! |
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