Question

What is the area of a right angle triangle with its hypotenuse and perimeter equal to x and y respectively?

Answer 1

Here's your answer :--
®®®®®®®®®®®®®®®®®®®®®®®®®®®®®®®

Let ABC be the right triangle.

Given, AC = x and perimeter of ΔABC = y

Perimeter of ΔABC = AB + BC + CA = y

∴ AB + BC + x = y

⇒ AB + BC = y – x

Squaring on both sides, we get

αв^2 + вc^2 + 2 × AB × BC = ( y – x)^2 ...(1)

In right ΔABC,

αв^2 + вc^2 = cα^2 = х^2 ...(2)

From (1) and (2), we get

х^2 + 2 × AB × BC = (y – x)^2

⇒ 2 × AB × BC = ч^2 + х^2 – 2xy – х^2 = ч^2 – 2xy
(ín thє fírѕt αttαchmєnt)

Area of ΔABC = × AB × BC

∴ Area of ΔABC = (Using(3))
(ín thє ѕєcσnd αttαchmєnt)

hσpє ít hєlpѕ!

(thєrє αrє 3 αttαchmєntѕ pσѕtєd...ѕσ kíndlч hαvє α lσσk αt αll σf 'єm)

ⓑⓔ ⓑⓡⓐⓘⓝⓛⓨ✌