Question

A wire, 112cm long, is bent to form a right angled triangle. if the hypotenuse is 50 cm long, find the area of the triangle.

Answer 1

Let the other 2 sides be x, y
Length of hypotenuse = 50 cm
Total length =112cm
x + y +50 =112
x + y =112 - 50
x + y = 62
By pythagorous theorem
x² + y² = 50²
x² + y² = 2500
(x + y)² - 2xy = 2500
-2xy = 2500 - 3844
= - 1344
xy = 1344/2
= 672
Area of triangle = 1/2xy
= 1/2*672
= 336
Therefore, area of the triangle = 336cm²
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Answer 2

336 cm²

Step-by-step explanation:

Let their length be 'x' and 'y'.

Total length of the wire would not change.  As now, it is a triangle.

∴ total length = perimeter of Δ

                 112 = x + y + 50

            62 - x = y          ...(1)

As this is a right angled triangle:  using Pythagoras theorem,

⇒ hypotenuse² = x² + y²

⇒ 50² = x² + (62 - x)²        {from(1)}

⇒ 2500 = x² + 3844 + x² - 124x

⇒ 0 = 2x² + 1344 - 124x

⇒ 0 = x² - 62x + 672

⇒ 0 = x² - 14x - 48x + 672

⇒ 0 = (x - 14)(x - 48)

  Hence, x = 14 or 48

when x = 14, y = 48

          x = 48, y = 14

Area = ½ xy = ½ * 48 * 14 = 336 cm²