Qstnid -A-11- One Of The Equal Sides Of An Isosceles Triangle Is 13 Cm And Its Perimeter Is 50 Cm. Find The Area Of The Triangle. - 20: Area Of Trapezium And A Polygon Class 8 Maths - Icse-viii-mathematics

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ICSE-VIII-Mathematics

20: Area of Trapezium and a Polygon Class 8 Maths

with Solutions - page 2

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#11
One of the equal sides of an isosceles triangle is 13 cm and its perimeter is 50 cm. Find the area of the triangle.
Ans : In isosceles ∆ABC
AB = AC = 13 cm But perimeter = 50 cm

∴ BC = 50 - (13 + 13) cm
= 50 - 26
= 24 cm
AD ⊥ BC
∴ AC = DC = 24/2 = 12 cm
In right ∆ABD,
AC² = AD² + BD² (Pythagoras Theorem)
⇒ (13)² = AD² + (12)²
⇒ 169 = AD² + 144
⇒ AD² = 169 - 144
= 25
= (5)²
∴ AD = 5 cm
Now area of ∆ABC = ½ × base × Altitude
= ½ × BC × AD
= ½ × 24 × 5
= 60 cm²