Question

# The measure of one side of a right triangle is 4.2m. If the difference of the lengths of hypotenuse and other is 14m, find the sides and area of the triangle.

Solution

## Let the perpedicular, p=4.2 m and base is b m, hypotenuse is h m. Then by the given question, h-b=14⇒h=b+14 Then by Pythagoros's theorem, p²+b²=h² or, (4.2)²+b²=(b+14)² or, 17.64+b²=b²+2.b.14+196 or, 17.64=28b+196 or, 28b=-178.36 or, b=-178.36/28 or, b=-6.37 Since any side of a triangle can't be negative that means the datas given are wrong. . I think 4.2 m is not the right length because if you add any two sides of a triangle, it should be greater than the third side. Here 4.2+(hypotenuse-14)=hypotenuse-9.8 which is shorter than the hypotenuse. It probably reads 42. Let x=length of the other side, then x+14=hypotenuse Apply Pythagoras theorem: 42²+x² = (x+14)² Expand the right-hand side: 1764+x²=x²+28x+196 28x=1764-196=1568 which gives x=56

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