Answer:
169 inches²
Explanations:
The length of each side of a square = √Area
The length of each side of the first square = √144 = 12inches
The length of each side of the second square = √25 = 5 inches
Let the length of each side of the third square be l
The right-angled triangle formed by joining the vertices of the three squares is shown below:
Using the Pythagora's theorem to find the length of each side of the third square:
[tex]\begin{gathered} l^2=12^2+5^2 \\ l^2=\text{ 144 + 25} \\ l^2=\text{ 169} \\ l\text{ = }\sqrt[]{169} \\ l\text{ = 13 inches} \end{gathered}[/tex]
The area of the third square is:
Area = l²
Area = 13²
Area = 169 inches²
