Answer
Small Square = $7$ inches side length
Large Square = $10$ inches side length
Work Step by Step
We are asked to find the side lengths of two squares given their combined areas.
First write the side lengths in relation to one another:
Small Square = $x$
Large Square = $(x+3)$
The area of the Small Square plus the area of the Large Square =$149$ in$^2$
$(x)^2 + (x+3)^2=149$
$x^2 + x^2 +3x+3x+9=149$
Combine like terms:
$2x^2+6x+9=149$
We can rewrite in standard quadratic equation form: $ax^2 + bx +c=0$
$2x^2+6x+-140=0$
With $a=2$, $b=6$,and $c=-140$
Now, apply the quadratic formula: $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$
$x=\dfrac{(-)6\pm\sqrt{6^2-4(2)(-140)}}{2(2)}$
$x=\dfrac{-6\pm\sqrt{36-8(-140)}}{4}$
$x=\dfrac{-6\pm\sqrt{36+1120}}{4}$
$x=\dfrac{-6\pm\sqrt{1156}}{4}$
$x=\dfrac{-6\pm34}{4}$
$x=\dfrac{-6+34}{4}$ or $x=\dfrac{-6-34}{4}$
$x=\dfrac{28}{4}$ or $x=\dfrac{-40}{4}$
$x=7$ or $x=-10$
Since the length of a physical object like a square can't be negative, we know that $x=7$
So, the length of the Small Square = $7$ and
the length of the Large Square = $(7+3)= 10$
