Question

Area of a right triangle is 54 cm. If one of its legs is 12 cm long, its perimeter is
(a) 18 cm
(b) 27 cm
(C) 36 cm
(d) 54 cm​

Answer 1

the perimeter of the right triangle is 36 cm

Answer 2

$\sf{\huge{\underline{\orange{Given :-}}}}$

• The area of a right triangle is 54 cm.

• One of its legs is 12 cm long.

$\sf{\huge{\underline{\green{To\:Find :-}}}}$

• The perimeter of a right triangle.

$\sf{\huge{\underline{ Solution :-}}}$

We know, The area of a right triangle

➝ ½ × base × hieght

According to the question,

The area of a right triangle is 54 cm.

➝ 54 = ½ × base × hieght

➝ 54 = ½ × 12 × hieght

➝ 54 = 6 × hieght

➝ hieght = 54 / 6

➝ hieght = 9 cm

In a right angle Δ ABC,

$\setlength{\unitlength}{1cm}\begin{picture}(6,5)\linethickness{.4mm}\put(1,1){\line(1,0){4.5}}\put(1,1){\line(0,1){3.5}}\qbezier(1,4.5)(1,4.5)(5.5,1)\put(.3,2.5){\large\bf 9}\put(2.8,.3){\large\bf 12}\put(1.02,1.02){\framebox(0.3,0.3)}\put(.7,4.8){\large\bf A}\put(.8,.3){\large\bf B}\put(5.8,.3){\large\bf C}\qbezier(4.5,1)(4.3,1.25)(4.6,1.7)\put(3.8,1.3){\large\bf \Theta }\end{picture}$

AC² = AB² + BC²

➝ AC² = 12² + 9²

➝ AC² = 144 + 81

➝ AC² = 225

➝ AC = √225

➝ AC = 15 cm

We know, The perimeter of a triangle is a + b + c

➝ 12 + 9 + 15

➝ 27 + 9

➝ 36 cm

The perimeter of a right triangle is 36 cm .

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