Question

In triangle ABC, angle B= 90°, AB = (2x+1) cm and BC= (x+1) cm, If the area of the triangle ABC is 60 cm, find its perimeter​

Answer 1

given :-

In triangle ABC, angle B= 90°, AB = (2x+1) cm and BC= (x+1) cm, If the area of the triangle ABC is 60 cm

to find :-

• perimeter

formula :-

$\dashrightarrow\sf \: area \: = \frac{1}{2} \times base \times height \:$

solution :-

$\dashrightarrow\sf \: \frac{1}{2} (x + 1)(2x + 1)$

$\dashrightarrow\sf \: \frac{1}{2} (2x^{2} + 3x + 1)$

given that area = 60cm²

so,

$\dashrightarrow\sf \: \frac{1}{2} (2x^{2} + 3x + 1) = 60$

$\dashrightarrow\sf \: 2x^{2} + 3x + 1 = 120$

$\dashrightarrow\sf \: 2x^{2} + 3x - 119 = 0$

so,

$\dashrightarrow\sf \: x = \frac{ - 3 + \sqrt{3^{2} - 4(2)( - 119)} }{2^{(2)} }$

$\dashrightarrow\sf \: \frac{ - 3 + 31}{4}$

$\dashrightarrow\sf \: 7( - 3( \frac{4}{4}x)$

$\dashrightarrow\sf \: 7$

so perimeter = AB + BC + CA

$\dashrightarrow\sf \: ca = \sqrt{ab^{2} + bc^{2} }$

$\dashrightarrow\sf \: ab = 2(7) + 1 = 15$

$\dashrightarrow\sf \: bc = 7 + 1 = 8$

$\dashrightarrow\sf \: ca = \sqrt{15^{2} + 8^{2} }$

$\dashrightarrow\sf \: 17$

$\dashrightarrow\sf \: perimeter = 15 + 8 + 17$

$\dashrightarrow\sf \: = 40cm \:$

so therefore perimeter = 40cm

so therefore our required answer is 40cm.