Question

The difference of length of 2 sides whichform a right angle triangle is 3 cmit's perimeter is 36 then find its area​

Answer 1

Step-by-step explanation:

Let the length of perpendicular be x.

Now, given that the difference of perpendicular and base = 3

⇒ Base = x + 3

Also, Perimeter = 36

⇒ 36 = x + (x + 3) + Hypotenuse

⇒ Hypotenuse = 36 – x – x – 3

⇒ 33 – 2x

Now, using Pythagoras Theorem,

Hypotenuse2 = Base2 + Perpendicular2

⇒ (33 – 2x)2 = x2 + (x + 3)2

⇒ 1089 + 4x2 – 132x = x2 + x2 + 9 + 6x

⇒ 2x2 – 1138x + 1080 = 0

Dividing whole equation by 2, we get –

⇒ x2 – 69x + 540 = 0

⇒ x2 – (60 + 9)x + 540 = 0

⇒ x2 – 60x – 9x + 540 = 0

⇒ x(x – 60) – 9(x – 60) = 0

⇒ (x – 60)(x – 9) = 0

⇒ x = 60 or x = 9

∵ Perimeter is given to be 36 cm

⇒ x(Perpendicular) = 9 cm

⇒ Base = x + 3

= 12 cm

Now,

⇒ 54 cm2

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