Question

If all the sides of a triangle are doubled then find
a)% increase in its area
b)no. of times area increased ​

Answer 1

Step-by-step explanation:

b) In a triangle let sides are a ,b, c , and (a+b+c)/2=s say , then area of the triangle =√{s(s-a)(s-b)(s-c)}

now if the sides are doubled then sides will be 2a, 2b, 2c , and (2a+2b+2c)/2=(a+b+c)=2s

then area of the triangle

=√{2s(2s-2a)(2s-2b)(2s-2c)}

=√{2×2×2×2×s(s-a)(s-b)(s-c)}

=4√{s(s-a)(s-b)(s-c)}

=4×area of smaller triangle .