Given:
The sides of a triangle are
6x2 and
(2x2−1) The area of the triangle is 84 sq. unit
Formula Used:
In a right angles triangle
Area of triangle
=(1∕2)× base
× perpendicular
Calculation:
Let
BC is base
So,
AB will be perpendicular
Now, According to the formula used
Area of triangle
=84 ⇒(1∕2)×(2x2−1)×6x2=84 ⇒(2x2−1)×x2−28=0 Let
x2=y So, The above equation can be written as
⇒(2y−1)×y−28=0 ⇒2y2−y−28=0 ⇒2y2−8y+7y−28=0 ⇒2y(y−4)+7(y−4)=0 ⇒(y−4)(2y+7)=0 ⇒y=4 or y=−7∕2 So,
x2=4 or
x2=−7∕2 [not possible]
⇒x=±2 So,
AB=6×22=24 and
BC=2×22−1=7 We know that
(7,24,25) is a triplet of a right-angled triangle
So, The hypotenuse will be 25
So, Perimeter
=(7+24+25) unit
=56 unit
∴ The perimeter of the triangle is 56 unit.