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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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