Question

The diagonal of a rectangle is 10. What is the area of the rectangle?
A. 24
B. 48
C. 50
D. 100
E. cannot be determined from the info given

Answer 1

E. You need one more side and angle.

Answer 2

or another side

Answer 3

Area = xy

x^2 + y^2 = 10^2

the possible sides form a circle with radius 10

Answer 4

These three rectangles have congruent diagonals.
As you can see their areas are quite different.
The conclusion is that just knowing the length of the diagonal of a rectangle is not enough information to find its area.

Answer 5

Note: If the sides have to be integers, then there is a unique answer.

Answer 6

if the diagonal is 10
we know the other 2 sides will be less than 10, that is
a < 10, b < 10

if you pick a value for either, you can get the value of the 2nd one by using pythagorean theorem

and regardless of what value you pick, so long is less than 10
the Area of the rectangle will remain the same

Answer 7

So I can't use the 30-60-90 triangle formula?

Answer 8

its kind of a trick question...by itself there is not enough info to know the Area
but since they give possible Areas, you can determine which possible Area is correct

example:
A = 48
8*6 = 48
and
8^2 + 6^2 = 100

Answer 9

say if I were to say pick for my side b = 5, my c = 10
that usually means a triangle of 30-60-90, meaning my \(\bf a = 5\sqrt{3}\)
using that I can find the area of that triangle, double that, and you get the area of the rectangle

Answer 10

the Area will be the same, no matter at what angle you arrange the diagonal, you see

Answer 11

because the diagonal carries a ratio for the other 2 sides

Answer 12

Ah I get it now! Thank you!

Answer 13

unless they tell you the sides are integer length, there is not enough info to know the area of the rectangle.

Answer 14

@jdoe, not to confuse the situation but by changing the angle (shape of rectangle) the Area does definitely changes

Answer 15

yes it does, ok, my bad, was triple checking