Question

A square has side length (x+5) units. What is it’s area

Answer 1

The area of square is $x^{2}+10 x+25$ square units

Solution:

Given that square has side length (x+5) units

To find: area of square

The area of square is given as:

$\text {Area of square }=\mathrm{a}^{2}$

Where "a" is the length of side

From question, length of each side "a" = x + 5 units

Substituting the value in above formula,

$\text {Area of square }=(x+5)^{2}$

${\text {Expanding }(x+5)^{2} \text { using the algebraic identity: }} \\\\ {(a+b)^{2}=a^{2}+2 a b+b^{2}}\end{array}$

$\begin{array}{l}{\text {Area of square }=x^{2}+2(x)(5)+5^{2}} \\\\ {\text {Area of square }=x^{2}+10 x+25}\end{array}$

Thus the area of square is $x^{2}+10 x+25$ square units