Question

Perimeter of any isoceles triangle is 544cm and length of each equal side is 5/6th of length of base. Let us write by calculating the area of this triangle.

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Answer 1

Answer:-

The area of the triangle is 13872 cm².

Explanation:-

Given :

Perimeter of the triangle = 544 cm

Length of each equal side = 5/6th of the length of base

To find :

The area of the Triangle

Solution :

Let the base be x cm

Length of each equal side= 5x/6 cm

We know that the formula of perimeter of an isoceles triangle is (a+b+c) cm.

$= > perimeter = 544 \: cm$

$= > \frac{5x}{6} + \frac{5x}{6} + x = 544 \: cm$

$= > \frac{5x + 5x + 6x}{6} = 544 \: cm$

$= > \frac{16x}{6} = 544 \: cm$

$= > x = \frac{544 \times 6}{16} \: cm$

$= > x = 204 \: cm$

Therefore, Length of sides :-

$= \frac{5}{6} \times 204 \: cm$

$= 170 \: cm$

Now, We have to find the height of the triangle.

Formula of finding the height of an isoceles triangle :-

Height= √(Length of equal side)² - (Half of the length of the base)² unit

=> Height= √170²-102² cn

=> Height= √28900-10404 cm

=> Height= √18496 cm

=> Height= 136 cm

Formula of finding the area of isoceles triangle=> (1/2 × base × height) square unit

=> Area= 1/2 × 204 × 136 cm²

=> Area= 13872 cm²