This Simple Math Mistake Fools Everyone! – Can You Solve It?

Added: 2026-05-15

[00:00:00]Hello everyone. You all welcome. Today we have a very interesting geometry math problem.

[00:00:07]Here we have given a right angle triangle whose one side is given which has a length of 12 + 9 units.

[00:00:14]And there is a square inside the triangle. Here our job is to find out the area of the square.

[00:00:22]Now, how can we find out the area of the square? We can find out the area of the square if we know that the length of its one side. As you know that the length of sides of a square are equal, so therefore let us suppose each side of the square is X units.

[00:00:39]So therefore, its all sides will be X units.

[00:00:43]So therefore, here we can write the area of the square as the area of the square that will become X * X which is X².

[00:00:57]So to find out the area of the square here we need the value of X², so we'll try to find out the value of X² from this figure.

[00:01:05]As we know that the angles in a square are always right angles. So therefore, here all of these four angles will be a right angles, 90° angles.

[00:01:18]Now, if this angle is a right angle, so this angle will be obviously a right angle. This is because the angles on a straight line is always 180°.

[00:01:29]And this is a right angle, so therefore this angle will be also a right angle.

[00:01:34]And looking to this one figure here, inside this bigger triangle there are two others right angle triangles, this one and this one.

[00:01:43]Looking to these two angles, this angle and this angle. These two angles are equal because they are corresponding angles.

[00:01:52]Now, in these two triangles here the two angles are equal.

[00:01:56]If two angles are equal, so the third angle will be must equal.

[00:02:02]So, here all the angles are equal in both the triangles. So, therefore, these two triangles are similar triangles.

[00:02:09]And we know that in similar triangles, the ratio among the corresponding sides are proportional and equal.

[00:02:16]So, here we will take the ratio of the corresponding sides of these two triangles. So, we'll take the ratio of their hypotenuse and the ratio of their bases.

[00:02:25]Here, the base of this triangle is X.

[00:02:28]This is not given.

[00:02:29]So, let us suppose this base is Y.

[00:02:34]So, therefore, from this figure here, we can write the ratio of their hypotenuse will become that become 9 by 12 is equal to and this will become X by Y.

[00:02:49]Let's cross multiply both numbers. So, this will become here this is 9 Y is equal to 12 X.

[00:03:00]And we'll take this 9 to the right hand side. So, this will become Y is equal to 12 X divided by 9.

[00:03:11]Here, we can simplify these two numbers here. 3 * 3 is 9 and 3 * 4 is 12.

[00:03:18]So, Y will become 4 X divided by 3.

[00:03:24]So, therefore, the base of this right angle triangle that will become as this is Y, so Y is 4 X divided by 3.

[00:03:34]Since our target is to find out the value of X, so here we need the value of X.

[00:03:39]Now, in this right angle triangle here, we have the values of its all sides.

[00:03:43]Hypotenuse, which is 12, perpendicular, which is X, and the base, which is 4 X by 3.

[00:03:49]So, So if we apply the Pythagoras theorem, so here we can very easily find out the value of x.

[00:03:55]So therefore here in this right angle triangle we will apply the Pythagoras theorem.

[00:04:00]And by Pythagoras theorem, the square of hypotenuse is equal to perpendicular square plus base square.

[00:04:07]So therefore this will become our hypotenuse is 12, this become 12 square is equal to perpendicular is x, this is x square plus our base is this is 4 x divided by 3 whole square.

[00:04:25]Let's simplify this one equation for the value of x. So here 12 square that is simply 144.

[00:04:34]This is x square plus and this expression will become this will become 4 x square divided by 3 square.

[00:04:45]Let's simplify this one expression, this one term.

[00:04:48]So this is 140 4 is equal to x square plus this will become 4 square, the 4 square is 16.

[00:04:59]x square divided by 3 square is 9.

[00:05:03]And we'll try to eliminate this 9 from the denominator. So therefore here we multiply all the terms by 9.

[00:05:10]So this will become this will become 144 times 9 is equal to this will become 9 x square and multiplying this expression with 9 here the 9 and 9 will be cancelled.

[00:05:26]This become only 16 x square.

[00:05:32]Let's multiply both the numbers. Here this is 9 * 4 is 36. This is 6, 3 will be carried. 9 * 4 is 36, 36 + 3 is 39.

[00:05:43]And 9 * 1 is 9, 9 + 3 it is 12.

[00:05:46]So, this gives him 1,296.

[00:05:50]Is equal to and there is x squared in the right hand side common, so we'll take out x squared as common.

[00:05:56]So, taking x squared common so we come 9 + 16.

[00:06:03]So, further this is 1,296 is equal to 9 + 16 it is 25.

[00:06:12]x squared As we need the value of x squared so therefore here we'll divide both side by 25.

[00:06:23]Here this 25 and this 25 will be cancelled so it become only x squared.

[00:06:30]And here dividing 1,296 by 25 it is gives him about 51.8 8 4.

[00:06:40]So, here we'll substitute this value in the area of square formula.

[00:06:45]That is area of square is equal to x squared.

[00:06:48]So, here the value of x squared it is simply 51.8 8 4 square units and that is the area of the square.