1.

Find the altitude and area of an isoscles triangle whose perimeter is 32cm and whose base is 12cm

Answer»

★Given:-

  • For an isosceles triangle,
  • Perimeter = 32cm
  • Base = 12cm

★To find:-

★Solution:-

Let the congruent sides of the isosceles triangle =a

The base =b  

We know,

✦Perimeter of the triangle = SUM of all sides

Putting values,

→a + a + b =32

→2a+12=32

→2a = 20

→a = 20/2

→a=10cm

Therefore,length of the congruent sides of the triangle is 10cm.

The altitude of the triangle divides it into two RIGHT angled triangles,

For each equal triangle,

  • Hypotenuse = 10 cm

Base = (12/2)

  • Base = 6 cm

By pythagoras theorem,

Height = √hypotenuse² - base²

              = √(10)² - (6)²

              = √100 - 36

              = √64

             = 8 cm

Therefore,altitude = 8 cm.

Using the FORMULA,

✦Area = 1/2(Base × Height)

Putting values,

→Area = (12 ×8)/2  cm²

→(96/2) cm²

→48 cm²

∴The area of the triangle is 48 cm².

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