Geometry

Triangles

Medium

The altitude drown to the base of an isosceles triangle is 16 cm and it's perimeter is 64 cm what is the area of triangle?

240 cm $^2$

140 cm $^2$

180 cm $^2$

192 cm $^2$

✅ Correct Option: 4

Let equal sides $a$ , base $b$ . Perimeter: $2a+b=64$ . Altitude bisects base, so $a^2=16^2+(b/2)^2$ . Substituting $a=32-b/2$ gives $1024-32b+b^2/4=256+b^2/4$ , so $b=24$ . Area $=\frac{1}{2}\times24\times16=192$ cm $^2$ .

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The altitude drown to the base of an isosceles triangle is 16 cm and it's perimeter is 64 cm what is the area of triangle?

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