Question

Please help me, I'm not sure what to do

Answer 1

Answer: 5.5

Step-by-step explanation: This problem uses the formula of the Pythagorean Theorem to solve for the length of the dotted line. To figure out the length of the dotted line, you must figure out what the side lengths of the rectangle are. From the diagram below, we can tell that the longer sides of the rectangle are unknown. To figure out how long those sides are, first find the length of the hypotenuse (longest side of a right triangle) of the triangle connected to the rectangle.

The formula to finding the length of the hypotenuse is:

a^(2)+b^(2)=c^(2)

c= the length of the hypotense of the right triangle

a & b = the lengths of the other two sides of the triangle

Simply plug in the two known lengths of the triangle into the formula and then simplify:

2^(2)+5^(2)=c^(2)

4+25=c^(2)

29=c^(2)

5.38516480713=c

Then, round the number to the nearest tenth.

c=5.4

Now that we know the length of the hypotenuse of the triangle connected to the rectangle, we know the lengths of the longest sides of the rectangle. In the diagram, you can see that the dotted line splits the rectangle in half, making two right triangles.

To find the length of the dotted line, simply plug in the known lengths of one of the triangles in the rectangle.

1^(2)+5.4^(2)=c

In this case, c now represents the length of the dotted line.

Simplify:

1+29.2=c

Note: 5.4^(2) technically is equal to 29.16, but the problem states that you must round to the nearest tenth. So, 29.16 rounded is 29.2.

30.2=c

c=5.5

Answer 2

5.5

Given :

• A rectangle adjacent to a triangle with it's one side = 1 unit & that of the triangle is base = 2 & perpendicular = 5

To find :

• The diagonal of the rectangle

Solution :

All we need to do in order to find out the length of the dotted line ( diagonal ) is firstly find the hypotenuse of the triangle which is equal to the other side of the rectangle and then use Pythagoras theorem to find out the length of the diagonal.

In the given triangle,

Using Pythagoras theorem,

• Hypotenuse = √[(Perpendicular)²+(base)²]
• Hypotenuse = √[(5)²+(2)²]
• Hypotenuse = √[25+4]
• Hypotenuse = √(29)
• Hypotenuse = 5.39

The hypotenuse of the triangle = other side of the rectangle.

In the given rectangle,

• The dotted line = √[(5.39)²+(1)²]
• The dotted line = √(29.05 + 1)
• The dotted line = √(30.05)
• The dotted line = 5.5

Therefore,the measure of the length of the dotted line would be equal to 5.5 .