Question

The ratio of equal and unequal side of an isosceles triangle is 3:5. If its
perimeter is 110 cm, then its area is
(a) 125 cm?
(b) 250 cm
(c) 250 11 cm
(d) 125./11 cm?
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Answer 1

The correct answer is option is (d).

Answer 2

Given,

The ratio of the equal and unequal sides of an isosceles triangle is 3:5 and the perimeter of the triangle is 110cm.

To find,

The area of the triangle?

Solution,

Let the side of equal side be 3x.

Let the side of the unequal side be 5x.

Perimeter of isosceles triangle = 2(Equal Sides) + Unequal Side

⇒   2(3x) + 5x = 110

⇒   6x + 5x = 110

⇒   11x = 110

⇒   x = 10.

Hence, the side of equal sides are = 3x = 3(10) = 30cm

The unequal side of the isosceles triangle = 5x = 5(10) = 50 cm.

The altitude of the isosceles triangle = $\sqrt{a^{2}-\frac{b^{2} }{4} }$.

$\sqrt{30^{2}-\frac{50^{2} }{4} }$, where a is the equal side and b is the unequal side.

⇒   16.58.

So, the height of isosceles triangle = 16.58cm

Now, Area of triangle =  ( 1/2 ) × Base × Height

⇒   Base = 50 cm

⇒   Height = 16.58

⇒   ( 1/2 ) × 50 × 16.58 = 414.5.

Hence, the area of the isosceles triangle = 414.5cm².