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Given c²= 25in², it can be known that c=5 in (taking only the positive square root);
b = 4in.
From the diagram, it can be seen that the triangle is a right-angled triangle.
For any right-angled triangle (a triangle in which one of the angles is 90 degrees), Pythagoras theorem holds good.
That is, the sum of the squares of two sides of a right-angled triangle would be equal to the square of the third side (the longest side, called the hypotenuse).
From the diagram, it can be seen that c is the longest side.
25 = b²+a²
It is given that b=4
25 = 4²+a²= 16 + a²
25 - 16 = a², 9=a²
Therefore, a=3in (Since the unit is inch).
Perimeter = a+b+c = 3+4+5 = 15 inches
Area of a triangle = 1/2 (base) x (height)
For any right-angled triangle,
area is given by the formula 1/2 (a)(b) where a and b are the two sides other than the hypotenuse.
Therefore, in this problem,
Area = 1/2 x (3) x(4) = 6 in²