Question

find the perimeter of an isosceles triangle if its base is 30 cm and area is 120 CM square​

Answer 1

The perimeter of an isosceles triangle = 64 cm

Step-by-step explanation:

Given,

The base of an isosceles triangle(b) = 30 cm and

The area of an isosceles triangle = 120 $cm^2$

Let the two equal sides of an isosceles triangle = a

To find, the perimeter of an isosceles triangle = ?

We know that,

The area of an isosceles triangle = $\dfrac{1}{4}b\sqrt{4a^{2}-b^2}$

⇒ $\dfrac{1}{4}\times 30\sqrt{4a^{2}-30^2}$ = 120

⇒ $\sqrt{4a^{2}-30^2} = 16$

Squaring both sides, we get

⇒ $4a^{2}-900 = 256$

⇒ $4a^{2}$ = 256 + 900 = 1156

⇒ $a^{2} = 289 = 17^2$

⇒ a = 17 cm

The perimeter of an isosceles triangle = (2a + b)

= 2 × 17 + 30 cm

= 64 cm

∴ The perimeter of an isosceles triangle = 64 cm

Answer 2

Step-by-step explanation:

Perimeter of isosceles triangle=30cm

Length of equal sides=12cm

Let third side of triangle=xcm

According to problem,

x+12+12=30

x+24=30

x=30−24

x=6

∴ Third side of triangle=6cm

Using Heron's formula

Area of triangle=

s(s−a)(s−b)(s−c)

sq. units

where s=

2

a+b+c

s=

2

30

=15

Area of triangle=

√15(15−12)(15−12)(15−6)

cm

2

=

√15×3×3×9

cm

2

=3×3×

15

cm

2

=9

15

cm

2

∴ Area of triangle=9

15

cm

2

.