Question

side of a triangle angled traingle is 3cm more than thrice the other side if the area of the triangle is 84 sq then find the hypotenuse of the triangle
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Answer 1

area = 1/2* base * height

84=1/2*x*x-3

84*2+3=x^2

under root 172=x

x=13.something

Answer 2

The measure of hypotenuse of Triangle is 4√35 cm  

Step-by-step explanation:

Given as :

For Right Angled Triangle

Area of Triangle = A = 84 sq cm

Let The measure of base = b = x cm

So, The measure of perpendicular = p = 3 x

Let The measure of hypotenuse = h cm

According to question

∵ Area of Triangle = 84 sq cm

And , Area of Triangle = $\dfrac{1}{2}$ × base × perpendicular

So, $\dfrac{1}{2}$ × base × perpendicular = 84

Or,  b × p = 84 × 2

Or,  x  × 3 x = 168

Or, x² = $\dfrac{168}{3}$

Or,  x²  = 56

∴   x = √56 = 2√14

So, The measure of base = b = 2√14 cm

So, The measure of perpendicular = p = 3 × 2√14 = 6√14 cm

Now, From Pythagoras Theorem

Hypotenuse² = Perpendicular² + Base²

i.e  h² = p² + b²

Or, h² = ( 6√14 cm) ² + ( 2√14 cm)²

Or, h² = 504 cm² + 56 cm²

Or,  h² = 560 cm²

∴    h = √560 cm

i.e h = 4√35 cm

So, The measure of hypotenuse = h =  4√35 cm

Hence,  The measure of hypotenuse is 4√35 cm  Answer