Question

the area of square is thirteen more than thrice its perimeter . how long is the side of area?

help me pls​

Answer 1

Answer:

13

Step-by-step explanation:

Area = A

Perimeter = P

Side = S

A = 3P + 13 (Eq. 1)

A = S^2 (Eq.2)

P = 4S (Eq. 3)

Substituting Equations 2 and 3 into 1:

S^2 = 3(4S) + 13

S^2 - 12S - 13 = 0

S^2 - 13S + S - 13 = 0 //breaking the middle term to solve the quadratic equation

S(S-13) + 1(S-13) = 0

(S+1)(S-13) = 0

S = - 1 and S = 13

Since the side cannot be a negative value, therefore it is 13 units in length.

Check:

A = 13^2 = 169

P = 4 x 13 = 52

169 = 3(52) + 13

169 = 156 + 13

169 = 169 hence proved

NOTE:

Alternately, you could simply form Eq. 1 and keep plugging in values till both sides are equal and you will find your length more quickly. Depends on what grade you are in and whether this question is in a subjective or objective section.