Question

the ratio of the equal sides to the base of an isosceles triangle is 3:1 if the perimeter of triangle is 28cm then find its area

Answer 1

Let equal sides = 3x
base = x
perimeter of an isosceles triangle = 28cm
2×3x + x = 28
6x + x = 28
7x = 28
x = 28/7
x = 4
So, equal sides is 3×4 =12cm
base is 4cm
area of an isosceles triangle = 1/4×4 root 4 × (12)square - (4)square
=root 4×144 - 16
=2×12-4
=24-4
=20cmsquare

Answer 2

Area of triangle is 23.66 cm²

Given:

The ratio of the equal sides to the base of an isosceles triangle is 3:1

Perimeter of the triangle = 28cm

To find:

The area of triangle

Solution:

Given that the ratio of the equal sides to the base of triangle is 3:1  

Let 3x is the length of equal side and x is the base of triangle

[ Since the ratio of length of equal side and the base 3 : 1 ]

Therefore, Perimeter of triangle = 3x + 3x + x = 7x

From given data 7x = 28 cm

⇒ x = 28/7 = 4 cm

⇒ Equal side of triangle = 3x = 3(4) = 12 cm

⇒ Base of the triangle = 4 cm

⇒ The altitude of the isosceles triangle h = √(a²− b²/4)

= √[144 - 16/4] = √144 - 4 = √140 = 11.83 cm

Altitude of the isosceles triangle = 11.83 cm

Area of triangle (A) = ½ × b × h  

= $\frac{1}{2} (4) (11.83)$ = 2(11.83) = 23.66 cm²

Area of triangle is 23.66 cm²

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