Question

The base of an isosceles
triangle is 16 cm and its area is 48 cm². The perimeter of the triangle is?​

Answer 1

✬ Perimeter = 36 cm ✬

Step-by-step explanation:

Given:

• Measure of base of an isosceles triangle is 16 cm.
• Area of the isosceles is 48 cm².

To Find:

• What is the perimeter of isosceles triangle?

Solution: Let ABC be an isosceles triangle where

• AC = BA {Since, two sides are equal}
• BC = 16 cm ( Base )
• AO = Perpendicular on BC

As we know that area of isosceles triangle is -

★ Area of an Isosceles triangle = 1/2 x Base x Height ★

A/q

$\implies{\rm }$ 48 = 1/2 x BC x AO

$\implies{\rm }$ 48 = 1/2 x 16 x AO

$\implies{\rm }$ 48 = 8 x AO

$\implies{\rm }$ 48/8 = AO

$\implies{\rm }$ 6 cm = AO

So, Height of the isosceles triangle is AO = 6 cm.

"We know that the perpendicular drawn on any side divides that side into two equal parts".

∴ BO = OC = 1/2 of BC

➟ BO = OC = 1/2 $\times$ 16

➟ BO = OC = 8 cm

Now, In right ∆AOC , applying Pythagoras Theorem

• AO = Perpendicular = 6 cm
• OC = Base = 8 cm
• AC = Hypotenuse

★ Pythagoras Theorem → Hypotenuse² = Base² + Perpendicular² ★

$\implies{\rm }$ AC² = OC² + AO²

$\implies{\rm }$ AC² = 8² + 6²

$\implies{\rm }$ AC² = 64 + 36

$\implies{\rm }$ AC² = 100

$\implies{\rm }$ AC = √100

$\implies{\rm }$ AC = 10 cm

So,measure of AC is 10 cm and BA = 10 cm ( Since, two sides are equal )

★ Perimeter of triangle = Sum of all sides ★

➱ Perimeter of ABC = AC + BC + BA

➱ Perimeter = ( 10 + 16 + 10 ) cm

➱ 36 cm

Hence, the perimeter of the isosceles triangle is 36 cm.