![\bold{\huge{\blue{\underline{ Solution }}}}](https://tex.z-dn.net/?f=%5Cbold%7B%5Chuge%7B%5Cblue%7B%5Cunderline%7B%20Solution%20%7D%7D%7D%7D)
<h3><u>Given </u><u>:</u><u>-</u></h3>
- <u>The </u><u>right </u><u>angled </u><u>below </u><u>is </u><u>formed </u><u>by </u><u>3</u><u> </u><u>squares </u><u>A</u><u>, </u><u> </u><u>B </u><u>and </u><u>C</u>
- <u>The </u><u>area </u><u>of </u><u>square </u><u>B</u><u> </u><u>has </u><u>an </u><u>area </u><u>of </u><u>1</u><u>4</u><u>4</u><u> </u><u>inches </u><u>²</u>
- <u>The </u><u>area </u><u>of </u><u>square </u><u>C </u><u>has </u><u>an </u><u>of </u><u>1</u><u>6</u><u>9</u><u> </u><u>inches </u><u>²</u>
<h3><u>To </u><u>Find </u><u>:</u><u>-</u></h3>
- <u>We </u><u>have </u><u>to </u><u>find </u><u>the </u><u>area </u><u>of </u><u>square </u><u>A</u><u>? </u>
<h3><u>Let's </u><u>Begin </u><u>:</u><u>-</u><u> </u></h3>
The right angled triangle is formed by 3 squares
<u>We </u><u>have</u><u>, </u>
- Area of square B is 144 inches²
- Area of square C is 169 inches²
<u>We </u><u>know </u><u>that</u><u>, </u>
![\bold{ Area \: of \: square = Side × Side }](https://tex.z-dn.net/?f=%5Cbold%7B%20Area%20%5C%3A%20of%20%5C%3A%20square%20%3D%20%20Side%20%C3%97%20Side%20%7D)
Let the side of square B be x
<u>Subsitute </u><u>the </u><u>required </u><u>values</u><u>, </u>
![\sf{ 144 = x × x }](https://tex.z-dn.net/?f=%5Csf%7B%20144%20%3D%20%20x%20%C3%97%20x%20%7D)
![\sf{ 144 = x² }](https://tex.z-dn.net/?f=%5Csf%7B%20144%20%3D%20%20x%C2%B2%20%7D)
![\sf{ x = √144}](https://tex.z-dn.net/?f=%5Csf%7B%20x%20%3D%20%E2%88%9A144%7D)
![\bold{\red{ x = 12\: inches }}](https://tex.z-dn.net/?f=%5Cbold%7B%5Cred%7B%20x%20%3D%2012%5C%3A%20inches%20%7D%7D)
Thus, The dimension of square B is 12 inches
<h3>
<u>Now, </u></h3>
Area of square C = 169 inches
Let the side of square C be y
<u>Subsitute </u><u>the </u><u>required </u><u>values</u><u>, </u>
![\sf{ 169 = y × y }](https://tex.z-dn.net/?f=%5Csf%7B%20169%20%3D%20%20y%20%C3%97%20y%20%7D)
![\sf{ 169 = y² }](https://tex.z-dn.net/?f=%5Csf%7B%20169%20%3D%20%20y%C2%B2%20%7D)
![\sf{ y = √169}](https://tex.z-dn.net/?f=%5Csf%7B%20y%20%3D%20%E2%88%9A169%7D)
![\bold{\green{ y = 13\: inches }}](https://tex.z-dn.net/?f=%5Cbold%7B%5Cgreen%7B%20y%20%3D%2013%5C%3A%20inches%20%7D%7D)
Thus, The dimension of square C is 13 inches.
<h3><u>Now, </u></h3>
It is mentioned in the question that, the right angled triangle is formed by 3 squares
The dimensions of square be is x and y
Let the dimensions of square A be z
<h3><u>Therefore</u><u>, </u><u>By </u><u>using </u><u>Pythagoras </u><u>theorem</u><u>, </u></h3>
- <u>The </u><u>sum </u><u>of </u><u>squares </u><u>of </u><u>base </u><u>and </u><u>perpendicular </u><u>height </u><u>equal </u><u>to </u><u>the </u><u>square </u><u>of </u><u>hypotenuse </u>
<u>That </u><u>is</u><u>, </u>
![\bold{\pink{ (Perpendicular)² + (Base)² = (Hypotenuse)² }}](https://tex.z-dn.net/?f=%5Cbold%7B%5Cpink%7B%20%28Perpendicular%29%C2%B2%20%2B%20%28Base%29%C2%B2%20%3D%20%28Hypotenuse%29%C2%B2%20%7D%7D)
<u>Here</u><u>, </u>
- Base = x = 12 inches
- Perpendicular = z
- Hypotenuse = y = 13 inches
<u>Subsitute </u><u>the </u><u>required </u><u>values</u><u>, </u>
![\sf{ (z)² + (x)² = (y)² }](https://tex.z-dn.net/?f=%5Csf%7B%20%28z%29%C2%B2%20%2B%20%28x%29%C2%B2%20%3D%20%28y%29%C2%B2%20%7D)
![\sf{ (z)² + (12)² = (169)² }](https://tex.z-dn.net/?f=%5Csf%7B%20%28z%29%C2%B2%20%2B%20%2812%29%C2%B2%20%3D%20%28169%29%C2%B2%20%7D)
![\sf{ (z)² + 144 = 169}](https://tex.z-dn.net/?f=%5Csf%7B%20%28z%29%C2%B2%20%2B%20144%20%3D%20169%7D)
![\sf{ (z)² = 169 - 144 }](https://tex.z-dn.net/?f=%5Csf%7B%20%28z%29%C2%B2%20%3D%20169%20-%20144%20%7D)
![\sf{ (z)² = 25}](https://tex.z-dn.net/?f=%5Csf%7B%20%28z%29%C2%B2%20%3D%2025%7D)
![\bold{\blue{ z = 5 }}](https://tex.z-dn.net/?f=%5Cbold%7B%5Cblue%7B%20z%20%3D%205%20%7D%7D)
Thus, The dimensions of square A is 5 inches
<h3>
<u>Therefore</u><u>,</u></h3>
Area of square
![\sf{ = Side × Side }](https://tex.z-dn.net/?f=%5Csf%7B%20%3D%20Side%20%C3%97%20Side%20%7D)
![\sf{ = 5 × 5 }](https://tex.z-dn.net/?f=%5Csf%7B%20%3D%205%20%C3%97%205%20%20%7D)
![\bold{\orange{ = 25\: inches }}](https://tex.z-dn.net/?f=%5Cbold%7B%5Corange%7B%20%3D%2025%5C%3A%20inches%20%7D%7D)
Hence, The area of square A is 25 inches.