Two sides of a triangle forming a right angle are 6‌mathrm‌x2 and left(2‌mathrm‌x2−1‌right). If the area of the triangle is 84 square units, then what is the perimeter of the triangle?
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.