Question

The base of an isosceles triangle measures 24cm and its area is 60 cm^2. Find its perimeter (Using Heron's formula).

Answer 1

A=bhb

2

P=2a+b

hb=a2﹣b2

4

Solving forP

P=b+b2+16(A

b)2=24+242+16·(60

24)2=50cm

Answer 2

Step-by-step explanation:

SOLUTION

Given :

Base of a isosceles triangle is 24 cm.

Area of a isosceles triangle is 60 cm².

Find :

The perimeter of isosceles triangle.

SO :

Let each equal side of isosceles triangle be a cm.

Then :

$s = \frac{a + a + 24}{2} \: cm$

$= > s = (a + 12)cm.$

By Heron's Formula :

$the \: area \: of \: triangle \: = \sqrt{s(s - a)(s - b)(s - c)}$

$= > \sqrt{(a + 12)(a + 12 - a)(a + 12 - a)(a + 12 - 24)} = 60(given)$

$= > \sqrt{(a + 12) \times 12 \times 12 \times (a - 12)} = 60$

$= > 12 \sqrt{(a + 12)(a - 12)} = 60$

$= > \sqrt{ {a}^{2} - 144 } = 5$

$= > {a}^{2} - 144 = 25$

$= > {a}^{2} = 169$

$= > a = 13.$

Hence :

The perimeter of isosceles triangle = 13cm + 13cm + 24cm = 50cm.