Question

The perimeter of a right angled triangle is $72cm$ and its area is $216{cm}^2.$ Find the sum of the lengths of its perpendicular sides (in $cm$).

• A. $36$
• B. $32$
• C. $42$
• D. $50$

Answer 1

The correct option is C $42$

REF.Image

Perimeter of right triangle = 72

a+b+c= 72 _____________ (1)

its area = 216

$\frac{1}{2}ba=216$

$ba=432$ ___________ (2)

$\therefore c^2=a^2+b^2$ (By pythagoras theorem )

$(a+b+c{)}^2=a^2+b^2+c^2+2ab+2bc+2ac$

$(72{)}^2=c^2+c^2+2ab+2bc+2ac$

$5184=2c^2+2ab+2bc+2ac$

$5184=2c^2+2ab+2c(b+a)$

$5184=2c^2+2ab+2c(72-c)$

$5184=2c^2+2ab+144c-2c^2$

$5184=2ab+144c$

$5184=2\times 432+144c$

$c=\frac{9320}{144}$

c=30

putting c in equation (1)

a+b+c=72

a+b=72-30

a+b=42.