How to find the length of the diagonal of a rectangle - ACT Math
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A rectangle has a height of 
and a base of 
. What is the length of its diagonal rounded to the nearest tenth?
A rectangle has a height of
1. Use Pythagorean Theorem with 
and 
.
2. Solve for 
, the length of the diagonal:
This rounds down to 
because the hundredth's place (
) is less than 
.
1. Use Pythagorean Theorem with
2. Solve for
This rounds down to
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The sides of rectangle ABCD are 4 in and 13 in.
How long is the diagonal of rectangle ABCD?
The sides of rectangle ABCD are 4 in and 13 in.
How long is the diagonal of rectangle ABCD?
A diagonal of a rectangle cuts the rectangle into 2 right triangles with sides equal to the sides of the rectangle and with a hypotenuse that is the diagonal. All you need to do is use the pythagorean theorem:
where a and b are the sides of the rectangle and c is the length of the diagonal.
A diagonal of a rectangle cuts the rectangle into 2 right triangles with sides equal to the sides of the rectangle and with a hypotenuse that is the diagonal. All you need to do is use the pythagorean theorem:
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Mark bought a TV at the store that was listed as 36in x 24in. He needs to figure out the diagonal to make sure the television is large enough but he left his measuring tape at his mother's house. What is the diagonal length of this television's screen in terms of inches?
Mark bought a TV at the store that was listed as 36in x 24in. He needs to figure out the diagonal to make sure the television is large enough but he left his measuring tape at his mother's house. What is the diagonal length of this television's screen in terms of inches?
Finding the diagonal of a rectangle is essentially a problem with triangles. If we set up a right triangle with legs 24 in. and 36 in., and set 
to be the diagonal (the hypotenuse), we can use the Pythagorean Theorem to solve for 
:
This comes out to be about 43.3 in.
Finding the diagonal of a rectangle is essentially a problem with triangles. If we set up a right triangle with legs 24 in. and 36 in., and set
This comes out to be about 43.3 in.
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A power company needs to run a piece of wire across a rectangular plot of land and must do so diagonally. The land is 
by 
in measurement. If it costs 
for each mile of wire deployed, how much is the expected cost of this project? Round to the nearest cent.
A power company needs to run a piece of wire across a rectangular plot of land and must do so diagonally. The land is
Notice that this problem could be represented as follows:
This means that you can find the distance of the wire merely by using the Pythagorean theorem:
Solving for 
, you get:
Thus, 
Using your calculator, multiply this by 
. This gives you approximately 
dollars in expenses.
Notice that this problem could be represented as follows:
This means that you can find the distance of the wire merely by using the Pythagorean theorem:
Solving for
Thus,
Using your calculator, multiply this by
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What is the diagonal of a rectangle with sides of length 
and 
? Round to the nearest hundredth.
What is the diagonal of a rectangle with sides of length
You could draw this rectangle as follows:
Solving for the diagonal merely requires using the Pythagorean theorem. Thus, you know:
or
, meaning that 
This is approximately 
Thus, the answer is 
.
You could draw this rectangle as follows:
Solving for the diagonal merely requires using the Pythagorean theorem. Thus, you know:
This is approximately
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What is the area of a rectangle with a diagonal of 
and one side that is 
?
What is the area of a rectangle with a diagonal of
Based on the description offered in the question, you know that your rectangle must look something like this:
Using the Pythagorean theorem, you can solve for the unknown side 
:
Thus, 
is 
. This means that the area is 
or 
.
Based on the description offered in the question, you know that your rectangle must look something like this:
Using the Pythagorean theorem, you can solve for the unknown side
Thus,
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