I have a rectangle 2.1m by 0.8m. What is the length of the diagonal to one decimal place?
To answer this, you will need to use the pythagorean therom, a2+b2=c2. a and b being the two side lengths, c will be your diagonal.
If a=2.1 and b=.8, the equation will be:
$${{\mathtt{2.1}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{0.8}}}^{{\mathtt{2}}} = {{\mathtt{c}}}^{{\mathtt{2}}}$$
Then you square 2.1 and 0.8
$${{\mathtt{2.1}}}^{{\mathtt{2}}} = {\frac{{\mathtt{441}}}{{\mathtt{100}}}} = {\mathtt{4.41}}$$
$${{\mathtt{0.8}}}^{{\mathtt{2}}} = {\frac{{\mathtt{16}}}{{\mathtt{25}}}} = {\mathtt{0.64}}$$
These values substituted into the equation give you:
$${\mathtt{4.41}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.64}} = {{\mathtt{c}}}^{{\mathtt{2}}}$$
When you add together 4.41 and 0.64, you get:
$${\mathtt{4.41}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.64}} = {\frac{{\mathtt{101}}}{{\mathtt{20}}}} = {\mathtt{5.05}}$$
You can then substitue this value into the equation giving you:
$${\mathtt{5.05}} = {{\mathtt{c}}}^{{\mathtt{2}}}$$
To get the c alone, you can take the square root of both sides, so:
$${{\mathtt{5.05}}}^{{\mathtt{0.5}}} = {\mathtt{2.247\: \!220\: \!505\: \!424\: \!423\: \!2}}$$(x^.5 is the same as taking the sqaure root of x)
The Sqaure root of c2 will be c, as the power of 2 will be cancled out by the square root.
So the final result will be
$${\mathtt{c}} = {\mathtt{2.247\: \!220\: \!505\: \!424\: \!423\: \!2}}$$
So back to your original question. In context, c is the diagonal of your rectangle. So when you take the value for c, rounded to the nearest tenth (one decimal place), your answer would be...
$${\mathtt{diagonal}} = {\mathtt{2.2}}$$
To answer this, you will need to use the pythagorean therom, a2+b2=c2. a and b being the two side lengths, c will be your diagonal.
If a=2.1 and b=.8, the equation will be:
$${{\mathtt{2.1}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{0.8}}}^{{\mathtt{2}}} = {{\mathtt{c}}}^{{\mathtt{2}}}$$
Then you square 2.1 and 0.8
$${{\mathtt{2.1}}}^{{\mathtt{2}}} = {\frac{{\mathtt{441}}}{{\mathtt{100}}}} = {\mathtt{4.41}}$$
$${{\mathtt{0.8}}}^{{\mathtt{2}}} = {\frac{{\mathtt{16}}}{{\mathtt{25}}}} = {\mathtt{0.64}}$$
These values substituted into the equation give you:
$${\mathtt{4.41}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.64}} = {{\mathtt{c}}}^{{\mathtt{2}}}$$
When you add together 4.41 and 0.64, you get:
$${\mathtt{4.41}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.64}} = {\frac{{\mathtt{101}}}{{\mathtt{20}}}} = {\mathtt{5.05}}$$
You can then substitue this value into the equation giving you:
$${\mathtt{5.05}} = {{\mathtt{c}}}^{{\mathtt{2}}}$$
To get the c alone, you can take the square root of both sides, so:
$${{\mathtt{5.05}}}^{{\mathtt{0.5}}} = {\mathtt{2.247\: \!220\: \!505\: \!424\: \!423\: \!2}}$$(x^.5 is the same as taking the sqaure root of x)
The Sqaure root of c2 will be c, as the power of 2 will be cancled out by the square root.
So the final result will be
$${\mathtt{c}} = {\mathtt{2.247\: \!220\: \!505\: \!424\: \!423\: \!2}}$$
So back to your original question. In context, c is the diagonal of your rectangle. So when you take the value for c, rounded to the nearest tenth (one decimal place), your answer would be...
$${\mathtt{diagonal}} = {\mathtt{2.2}}$$