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The area of the isosceles triangle is 5/4 √11 cm² , if the perimeter is 11 cm and the base is 5 cm. Is the given statement true or false and justify your answer.

Solution:

Given, area of isosceles triangle = 5/4 √11 cm²

Perimeter = 11 cm

Base = 5 cm

We have to determine if the given statement is true or false.

We know that in an isosceles triangle two sides are of equal length.

So, a = 5 cm

Perimeter = equal side + equal side + base

11 = 2(equal side) + 5

2(equal side) = 11 - 5

2(equal side) = 6

Equal side = 6/2

Equal side = 3 cm

So, b = 3 cm

Area of isosceles triangle = a/4 √4b² - a²

= 5/4 √4(3)² - (5)²

= 5/4 √4(9) - 25

= 5/4 √36 - 25

= 5/4 √11

Area = 5/4 √11 cm²

Therefore, the given statement is true.

✦ Try This: Write True or False and justify your answer: The area of the isosceles triangle is 28√13 cm² , if the perimeter is 13 cm and the base is 3 cm.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 12

NCERT Exemplar Class 9 Maths Exercise 12.2 Problem 3

The area of the isosceles triangle is 5/4 √11 cm² , if the perimeter is 11 cm and the base is 5 cm. Is the given statement true or false and justify your answer.

Summary:

The given statement “The area of the isosceles triangle is 5/4 √11 cm² , if the perimeter is 11 cm and the base is 5 cm” is true

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