The altitude drawn to the base of an usisceles triangle us 8 cm and the perimeter is 32 cm. Find the area of the triangle.
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let ABC be the isosceles triangle, the AD be the altitude
Let AB = AC = x then BC= 32-2x [because parameter = 2 (side) + Base]
since in an isoceles triange the altitude bisects the base so
BD = DC = 16-x
In a triangle ADC, (AC)2=AD^2+DC^2
x2=8^2+(16−x)^2x2=8^2+16-x2 ⇒x=10⇒x=10
BC = 32-2x = 32-20 = 12 cm
Hence, required area = 1/2*BC*AD= 1/2*12*10 = 60 sq cm
Let AB = AC = x then BC= 32-2x [because parameter = 2 (side) + Base]
since in an isoceles triange the altitude bisects the base so
BD = DC = 16-x
In a triangle ADC, (AC)2=AD^2+DC^2
x2=8^2+(16−x)^2x2=8^2+16-x2 ⇒x=10⇒x=10
BC = 32-2x = 32-20 = 12 cm
Hence, required area = 1/2*BC*AD= 1/2*12*10 = 60 sq cm
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