Games
Problems
Go Pro!

Triangle in a Square

Pro Problems > Math > Geometry > Triangles
 

Triangle in a Square

Triangle ABC is inside square ABDE, and C lies along side DE. If the area of the triangle is 24 square units, what is the length of AB?

Presentation mode
Problem by allie

Solution

In order to make it feasible for teachers to use these problems in their classwork, no solutions are publicly visible, so students cannot simply look up the answers. If you would like to view the solutions to these problems, you must have a Virtual Classroom subscription.
Assign this problem
Click here to assign this problem to your students.

Similar Problems

Triangle in a Square

A triangle is placed on the interior of a square so that two of the triangle's vertices lie on two adjacent vertices of the square, and the third vertex lies on the opposite side,
1
3
of the way between the two endpoints.

If the perimeter of the triangle (in linear units) is equal to the area of the triangle (in square units), what is the length of the side of the square?

Angles in a Triangle

In a triangle, the measure of the largest angle is 12 less than the sum of the measures of the other two angles. The largest angle is also 52 more than the twice the middle angle decreased by three times the smallest angle. What is the largest angle measure?

Angle Measure

Line segment AB is intersected by segment DC, with D on AB, between A and B. 

In triangle ADC, m∠ADC = 30º + x and  m∠DAC = 50º

In triangle ABC, m∠ACB = 115º + x

In triangle CDB, m∠CDB = 140º + x

Find m∠CBD.

Two Triangles with Angle Measures

In a triangle, the angles measures are: 3x + 44, x, and 2x - 20. In a second triangle, two of the angle measures are x + 20 and 2x - 5. What is the measure of the third angle?

Triangle Variables

An isosceles triangle is a triangle in which two of the angles have the same measure. In an isosceles triangle, the angle measures are 30 + x, 62 - x, and 10 + 2x + y. What are the possible numeric values for the measures of the angles?

Angle Riddle

The angles of a triangle meet the following criteria:

  • All the angle measures are prime numbers.
  • All the angle measures are distinct.
  • Exactly two of my angle measures are palindromic.
  • The difference between my two largest angle measures is a two digit number x.
  • One of the digits of x is twice the other digit.

Three Two-Digit Angle Measures

The measures of the angles in a triangle are all two digit numbers, and two of them end in 3. Exactly two of them contain the digit 4. None of the angle measures are multiples of three. What are the measures of the angles?

Three Triangles

The angles in a triangle have measures x, x + 10, and y.

The angles in a second triangle have measures x + y, 40, and 50.

The angles in a third triangle have measures x – y, 40, and z.

What is the value of z?

Triangle and Rectangle

In the diagram displayed, the triangle splits the rectangle into three similar triangles. Find the value of AD2 divided by the product of DE and EC.

Quadratic Triangle

The angles in a triangle have measures x2 - 5, 2x + 18, and x + 37. What is the measure of the largest angle in the triangle?
 

Angle Bisector, Arithmetic Angles, Split Triangle, Forty-five and Thirty

Featured Games on This Site

Match color, font, and letter in this strategy game
Trap all the dots in this problem-solving puzzle

Blogs on This Site

Reviews and book lists - books we love!
The site administrator fields questions from visitors.
Like us on Facebook to get updates about new resources
Home
Pro Membership
About
Privacy