Question

the base of an isosceles triangle measures of 80 cm and its area is 360cm.find the perimeter of the triangle

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Perimeter = 162 cm

Step-by-step explanation:

Given:

• Measure of base of isosceles triangle is 80 cm.
• Area of isosceles triangle is 360 cm².

To Find:

• What is the perimeter of triangle ?

Solution: Let the length of height of isosceles triangle be x cm .

As we know that

Area of ∆ = 1/2 × Base × Height

A/q

• Area is 360 cm².

$\implies{\rm }$ 1/2 × 80 × x = 360

$\implies{\rm }$ 40x = 360

$\implies{\rm }$ x = 360/40

$\implies{\rm }$ x = 9

So the measure of height of triangle is 9 cm.

Now in the triangle AE is a perpendicular to base BC.

∴ BE = 1/2 × BC = 1/2 × 80 = 40 cm

Now, in right angled triangle AEB , by Pythagoras theorem

AB² = AE² + BE²

AB² = 9² + 40²

AB² = 81 + 1600

AB = √1681 = 41

Opposite sides of an isosceles triangle are equal to each other. Therefore AB = AC = 41 cm.

∴ Perimeter of ∆ = Sum of all sides

➮ Perimeter = 41 + 41 + 80

➮ 162 cm

Hence, Perimeter of isosceles triangle is 162 cm.