1.

The perimeter of a triangle is 40 cm and its area is 60 cm2. If the largest side measures 17 cm, then the length (in cm) of the smallest side of the triangle is1). 42). 63). 84). 15

Answer»

Let a, b and c be the LENGTHS of the triangle.

Let ‘a’ be the greatest side with LENGTH 17 cm and c be the smallest length.

Given, Perimeter of triangle = 40 cm

⇒ (sum of all sides) = 40

⇒ a + b + c = 40

⇒ 17 + b + c = 40

⇒ b + c = 23

Then semi-perimeter:

⇒ s = Perimeter/2

= 40/2 cm

= 20 cm

We know that,

Area of triangle = $(\sqrt {s\left( {s - a} \right)\left( {s - b} \right)\left( {s - c} \right)})$

Where, s is semi perimeter and a, b and c are sides of the triangle

$(\Rightarrow 60 = \sqrt {20 \times \left( {20-17} \right) \times \left( {20-b} \right) \times \left( {20-\left( {23-b} \right)} \right)})$

Squaring both sides

⇒ 3600 = 60 × (20 - b) × (b - 3)

⇒ 60 = -b2 + 23b – 60

⇒ b2 – 23b + 120 = 0

Solving above we get,

b = 15 or 8

So if b = 15CM then,

⇒ c = 23 – 15

= 8 cm

And if b = 8 cm then,

⇒ c = 23 – 8

= 15 cm

Since C is the smallest side of triangle thus its length MUST be 8 centimeters.


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