Question

A side of a right angled triangle is 3cm more than thric the other side. if the area of the triangle is 84sq.cm,then find the hypotenuse of the triangle ​

Answer 1

Answer:

See attachment please

Answer 2

Answer:

The value of Hypotenuse is 12.20 centimeter

Step-by-step explanation:

Given as :

For a right angled triangle ,

Let The three sides be AB = a , BC = b , CA = c

Let The hypotenuse = CA

Height = AB

Base = BC

The measure of one side = 3 cm + 3 ×The measure of other side

So, Let AB = 3 cm + 3 × BC

i.e a = 3 cm + 3 × b                ...........1

Again

The area of the right angle triangle = A = 84 square centimeter

We know that

Area of triangle = $\dfrac{1}{2}$ × height × base

So, A =  $\dfrac{1}{2}$ × AB × BC

Or, A =  $\dfrac{1}{2}$ × a × b

Or , 84 =  $\dfrac{1}{2}$ × (3 ×b + 3 ) × b       (putting value of a)

Or, 84 × 2 = 3 b² + 3 b

Or, 3 b² + 3 b - 168 = 0

Solving this quadratic equation while comparing with ax² + bx + c = 0

x = $\dfrac{- b\pm \sqrt{b^{2} - 4\times a\times c}}{2\times a}$

So, b = $\dfrac{- 3\pm \sqrt{3^{2} - 4\times 3\times -168}}{2\times 3}$

Or, b = 7 , - 8

So, The value of base = b = 7 cm

And The value of height = 3 cm + 7

i.e The value of height = 3 + 7 = 10 cm

Now, As we know that , In a right angled triangle

Hypotenuse² = Perpendicular² + Base²

So, Hypotenuse² = height² + Base²

Or, Hypotenuse² = (10)² + (7)²

Or, Hypotenuse² = 100 + 49

Or, Hypotenuse² = 149 cm

∴ Hypotenuse = √149

Or,  Hypotenuse = 12.20 cm

So, The value of Hypotenuse = 12.20 cm

Hence, The value of Hypotenuse is 12.20 centimeter . Answer