Question

the base of the isosceles triangle is 24 cm area is 192 cm. find the perimeter

Answer 1

Formula of area of triangle is 1/2 X base X height

Hence 1/2 X 24 X h = 192

We get h as 16 cm

Now in an isoceles triangle, the HT, half of base and the equal sides form and right angled triangle. So using Pythagoras,

16^2 + (24/2)^2 = side ^2

We get the side as 20 cm.

Now perimeter will be 24+20+20 = 64 cm

Answer 2

Be =24
Area=192
Altitude = 24×x×1/2=192
24×x=192×2
24 ×x=384
x=384/24
x=16
Height of the triangle divides the isosceles triangle into two right triangles
The we have 16^2×24/2^2=AB^2
256+144=AB^2 =400
Therefore AB=20
Perimeter of the triangle =side+side +side =20+20+24=64