Question

The area of a triangle is 60 square units. If two of its sides are 8 units and 17 units, then the third side is

Answer 1

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Answer 2

Given:

The area of a triangle is 60 square units. If two of its sides are 8 units and 17 units.

To find:

The length of the 3rd side.

Calculation:

Let's consider ∆ABC , and altitude dropped from vertex A be AD such that;

AB = 17 cm , BC = 8 cm

Area of the Triangle will be ;

$Area = \dfrac{1}{2} \times (base)\times (altitude)$

$=>Area = \dfrac{1}{2} \times (BC)\times (AD)$

$=>60 = \dfrac{1}{2} \times (8)\times (AD)$

$=>AD = \dfrac{60}{4}$

$=>AD = 15 cm$

Now , applying Pythagoras Theorem in ∆ABD;

${AB}^{2}={AD}^{2}+{BD}^{2}$

$=>{(17)}^{2}={(15)}^{2}+{BD}^{2}$

$=>289=225+{BD}^{2}$

$=>{BD}^{2}=64$

$=>BD = 8 cm$

$=>BD = BC = 8 cm$

So , we can say that BD and BC are coinciding such that AD and AC also coincide.

So, the 3rd side is 15 cm.

An alternative method that can be used:

• Consider the other side to be "d" and apply Heron's formula.

• Solve the bi-quadratic Equation and get the value of "d".

• Another possible solution will be √481 cm $\approx\:$ 21.93 cm.

To see the solution with alternative method , click here:

https://brainly.in/question/21592777