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I have a rectangle 2.1m by 0.8m. What is the length of the diagonal to one decimal place?

 Dec 8, 2014

Best Answer 

 #1
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+5

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...

$${\mathtt{diagonal}} = {\mathtt{2.2}}$$

 Dec 8, 2014
 #1
avatar
+5
Best Answer

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...

$${\mathtt{diagonal}} = {\mathtt{2.2}}$$

Guest Dec 8, 2014
 #2
avatar+130511 
0

Very well presented, Anonymous.....why don't you join up as a member???

 

 Dec 8, 2014

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