Question

Find the area of the remaining square and the sides of the triangle.100х64

Answer 1

The diagram shows two square having area

`\begin{gathered} 100\text{ square unit for the bigger square } \\ 64\text{square for the other smaller square} \end{gathered}`

Using the formula for the area of a square, the lenght of each side will be

`\begin{gathered} \text{Area}=l^2 \\ 100=l^2 \\ l=\sqrt[]{100}=10units \end{gathered}`

Similarly for the other square with area 64 square units, the side will have the lenght

`\begin{gathered} \text{Area}=l^2 \\ 64=l^2 \\ l=\sqrt[]{64}=8units \end{gathered}`

These side correspounding with the hypotenuse sides and one of the legs of the right angle triangles,

hence using the pythagoras theorem, we can obtain the other leg with correspound to the area of the remaining square

`\begin{gathered} by\text{ pathagoras rule } \\ 10^2=8^2+x^2 \\ x^2=100-64 \\ x^2=36 \\ x=\sqrt[]{36}=6units \end{gathered}`

Then the sides of the triagle will be

`6\text{units,}8\text{units and 10unit}`

Then the area of the remaining square will be obtained by using the smalles sides which is 6units

`\begin{gathered} \text{Area}=l^2 \\ \text{Area}=6^2 \\ \text{Area}=36\text{ square unit} \end{gathered}`

Therefore the Area of the remaining square is 36 square unit and the triangle has the sides 6unit, 8units and 10unit