the perimeter of an isosceles triangle is 100 cm. if each of its equal sides is 26 cm. Find the area of the triangle
Answers
The perimeter of an isosceles triangle is 100 cm.
if each of its equal sides is 26 cm
∴ third side [base]=100-[26+26] =48 cm
semi perimeter [s] =[a+b+c]/2
[s] =[100]/2 =50
If you know the length of three sides of the triangle, the area of the triangle is A=√[s∗(s−a)∗(s−b)∗(s−c)]
A=√[50∗(50−26)∗(50−26)∗(50−48)]
A=√[50∗24∗24)∗2]
A=√[50∗24∗24)∗2]
A=√57600 =240 cm² ANS
ALTERNATELY short cut method
If′a′is the equal side and′b′is the base
Area=b∗√(4*a^2−b^2)/4
Area=48∗√(4*26^2−48^2)/4
Area=48∗√(2704−2304)/4
Area=48∗√400/4
Area=48∗20/4
Area=240 cm² ANS
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Given,
a = 26 cm
The perimeter = 100 cm.
if each of its equal sides is 26 cm
∴ third side b =100-26*2 =48 cm
Perimeter of an isosceles triangle
Altitude of an isosceles triangle
= √a^2–[b^2/4] cm
= √26^2–[48^2/4] cm
=√676-576 cm
=√100 =10 cm
Area of an isosceles triangle
= b×h/2
= 48×10/2
=240cm² ANS