Given that 5x:8 = 7:2 Calculate the value of x.
2 answers:
You might be interested in
Answer:
If both sides are integers, one side will be 4 feet and the other will be 6 feet. The other solution is the symmetrical solution (4 feet instead of 6 feet, and 6 feet instead of 4 feet).
Step-by-step explanation:
We have a rectangular blanket, that has a diagonal that measures h=7.21 feet.
The two sides of the rectangle a and b can be related to the diagonal h by the Pithagorean theorem:
Then, we can express one side in function of the other as:
Then, if we define b, we get the value of a that satisfies the equation.
A graph of values of a and b is attached.
If both side a and b are integers, we can see in the graph that are only two solutions: (b=4, a=6) and (a=4, b=6).
I draw the two triangles, see the picture attached.
As you can see, angle 1 and 2 are vertically opposite angles because they are formed by the same two crossing lines and they face each other.
Angles <span>ABQ and QPR, as well as angles BAQ and QRP, are alternate interior angles because they are formed by </span><span>two parallel lines crossed by a transversal, and they are inside the two lines on opposite sides of the transversal.</span>
Hence, Allison's correct claims are:
1 = 2 because they are vertically opposite angles.
BAQ = QRP because they are alternate interior angles.
Therefore Allison, in order to prove her claim, can use the AA similarity theorem: if two angles of a triangle are congruent to two angles of the other triangle, then the two triangles are similar.
As you can see, angle 1 and 2 are vertically opposite angles because they are formed by the same two crossing lines and they face each other.
Angles <span>ABQ and QPR, as well as angles BAQ and QRP, are alternate interior angles because they are formed by </span><span>two parallel lines crossed by a transversal, and they are inside the two lines on opposite sides of the transversal.</span>
Hence, Allison's correct claims are:
1 = 2 because they are vertically opposite angles.
BAQ = QRP because they are alternate interior angles.
Therefore Allison, in order to prove her claim, can use the AA similarity theorem: if two angles of a triangle are congruent to two angles of the other triangle, then the two triangles are similar.