Triangle square area
A right triangle has an area of 36 cm2. A square is placed in it so that two sides of the square are parts of two sides of a triangle, and one vertex of the square is in a third of the longest side.
Determine the area of this square.
Determine the area of this square.
Final Answer:
Showing 1 comment:
Math student
Given: (ab)/2 = 36; ab = 72
Let: c = sqrt(aˆ2 + bˆ2)
(b-x)/(c/3) = x/((2c)/3)); b = (3x)/2
(a-x)/((2c)/3)) = a/c; a = 3x
ab = (3x)((3x)/2) = 72
Therefore, xˆ2 = 16.
Let: c = sqrt(aˆ2 + bˆ2)
(b-x)/(c/3) = x/((2c)/3)); b = (3x)/2
(a-x)/((2c)/3)) = a/c; a = 3x
ab = (3x)((3x)/2) = 72
Therefore, xˆ2 = 16.
Tips for related online calculators
See also our right triangle calculator.
You need to know the following knowledge to solve this word math problem:
algebraarithmeticplanimetricsthemes, topicsGrade of the word problem
Related math problems and questions:
- An equilateral
An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle? - Sides in ratio
The sides of the triangle are in a ratio of 2:6:5. Find the dimensions of the remaining sides if the longest side is 32 cm. - Triangle perimeter
Calculate the triangle perimeter whose sides are in ratio 3:5:7 and the longest side is 17.5 cm long. - Triangle height intersection
Given a triangle ABC: A (-1,3), B(2,-2), C(-4,-3). Determine the coordinates of the intersection of the heights and the coordinates of the intersection of the axes of the sides. - Trapezoid RT
The plot is a rectangular trapezium ABCD, where ABIICD has a right angle at the vertex B side and AB has a length of 36 m. The lengths of the sides AB and BC are in the ratio 12:7. The lengths of the sides AB and CD are in the ratio 3:2. Calculate the con - Integer sides
A right triangle with an integer length of two sides has one leg √11 long. How long is its longest side? - Quadrilateral triangle segment
The quadrilateral ABCD is symmetrical about the diagonal AC. The length of AC is 12 cm, the length of BC is 6 cm, and the interior angle at vertex B is right. points E and F are given on the sides AB, and AD so that the triangle ECF is equilateral. Determ
