Calculating the length of the diagonal of a rectangle - GMAT Quantitative Reasoning
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A rectangle has a length of 
and a width of 
. What is the length of the diagonal of the rectangle?
A rectangle has a length of
If the rectangle has a length of 
and a width of 
, we can imagine the diagonal as being the hypotenuse of a right triangle. The length and width are the other two sides to this triangle, so we can use the Pythagorean Theorem to calculate the length of the diagonal of the rectangle:
If the rectangle has a length of
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is a rectangle, 
and 
. What is the length of the diagonal of the rectangle?
Here, we also have a 
triangle, indeed both ADC and ABD are 
triangles. We can see that by calculating the missing angles. in each triangle we find that this angle to be 30 degrees. Since 
, we also know that the other sides of the triangles will be 
and 
, since a 
triangle have its sides in ratio 
, where 
is a constant. In this case 
. Therefore the hypotenuse will be 
, which is also the length of the diagonal of the rectangle.
Here, we also have a
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A rectangle has a length of 
and a width of 
. What is the length of the diagonal of the rectangle?
A rectangle has a length of
The diagonal of a rectangle can be thought of as the hypotenuse of a right triangle with the length and width of the rectangle as the other two sides. This means we can use the Pythagorean theorem to solve for the diagonal of a rectangle if we are given its length and its width:
The diagonal of a rectangle can be thought of as the hypotenuse of a right triangle with the length and width of the rectangle as the other two sides. This means we can use the Pythagorean theorem to solve for the diagonal of a rectangle if we are given its length and its width:
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Rectangle 
has an area of 
and 
. What is the length of the diagonal 
?
Rectangle
Firstly, before we try to set up an equation for the length of the sides and the area, we should notice that the area is a perfect square. Indeed 
. Now let's try to see whether 13 could be the length of two consecutive sides of the rectangle, Indeed, we are told that 
, therefore ABDC is a square with side 13 and with diagonal 
, where 
is the length of the side of the square. Therefore, the final answer is 
.
Firstly, before we try to set up an equation for the length of the sides and the area, we should notice that the area is a perfect square. Indeed
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Rectangle 
, has area 
and 
. What is the length of diagonal 
?
Rectangle
To find the length of the sides to calculate the length of the diagonal with the Pythagorean Theorem, we would need to set up two equations for our variables. However, trial and error, in my opinion in most GMAT problems is faster than trying to solve a quadratic equation. The way we should test values for our sides is firstly by finding the different possible factors of the area, that way we can see possible factors.
As follows 
has possible factors 
. From these values we should find the two that will give us 8, the length of the two consecutive sides.
We find that 
and 
are the values for the two sides.
Now we just need to apply the Pythagorean Theorem to find the length of the diagonal: 
, or 
.
To find the length of the sides to calculate the length of the diagonal with the Pythagorean Theorem, we would need to set up two equations for our variables. However, trial and error, in my opinion in most GMAT problems is faster than trying to solve a quadratic equation. The way we should test values for our sides is firstly by finding the different possible factors of the area, that way we can see possible factors.
As follows
We find that
Now we just need to apply the Pythagorean Theorem to find the length of the diagonal:
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Find the length of the diagonal of a rectangle whose sides are lengths 
.
Find the length of the diagonal of a rectangle whose sides are lengths
To find the diagonal, you must use the pythaorean theorem. Thus:
To find the diagonal, you must use the pythaorean theorem. Thus:
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Calculate the length of the diagonal of a rectangle whose width is 
and length is 
.
Calculate the length of the diagonal of a rectangle whose width is
To solve, simply use the Pythagorean theorem.
To solve, simply use the Pythagorean theorem.
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If a garden bed will have side lengths of 9 meters and 12 meters, what will the distance be across its diagonal?
If a garden bed will have side lengths of 9 meters and 12 meters, what will the distance be across its diagonal?
If a rectangular garden bed will have side lengths of 9 meters and 12 meters, what will the distance be across its diagonal?
This question is a rectangle question, but it could also be seen as a triangle question. If we have a rectangle with two side lengths, we can find the diagonal by using Pythagorean theorem:
If you are feeling really observant, you may have seen that we have a Pythagorean triple. In this case, a 3-4-5 triangle. You could have skipped using Pythagoran theorem and simply done three times five to get fifteen meters.
If a rectangular garden bed will have side lengths of 9 meters and 12 meters, what will the distance be across its diagonal?
This question is a rectangle question, but it could also be seen as a triangle question. If we have a rectangle with two side lengths, we can find the diagonal by using Pythagorean theorem:
If you are feeling really observant, you may have seen that we have a Pythagorean triple. In this case, a 3-4-5 triangle. You could have skipped using Pythagoran theorem and simply done three times five to get fifteen meters.
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