# Triangle in a Square

Pro Problems > Math > Geometry > Triangles## Triangle in a Square

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?

## Solution

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The angles of a triangle meet the following criteria:

- All the angle measures are prime numbers.
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m ∠DCF = 80

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m ∠FBD = 50.

If segment BF bisects ∠ABD, find m ∠BAC.

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

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In triangle ABC, m∠ACB = 115º + x

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Find m∠CBD.

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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?

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In the diagram displayed, the triangle splits the rectangle into three similar triangles. Find the value of AD^{2} divided by the product of DE and EC.

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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?

### Split Triangle

Segment AD is drawn in triangle ABC, with D on side BC. Given the following information, determine the measure of angle ADB.

measure of angle BAD = x

measure of angle CAD = 2x

measure of angle ADC = 2y

measure of angle ABD = y

measure of angle ACD = x + y