Dragan

R₁ - R₂ - R₃ + R₄ = 120  

w( 2w - 4) = 96

w = 8 inches

∠DBC = ( 360 - 136 - 120 ) / 2

The perimeter of an equilateral triangle is 9 inches more than the perimeter of a​ square, and the side of the triangle is 6 inches longer than the side of the square. Find the side of the triangle.

The perimeter of the square is:   4x 

The perimeter of the triangle is:   3 ( x + 6 )      or       4x + 9

4x + 9 = 3 ( x + 6 ) 

140 ???

Let a triangle ABC with BC = 6 cm and the area of 30 cm2. A square PQRS is inscribed so that points S and R is on BC, Q on AC, and P on AB  respectively. Find the side length of the square PQRS.

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Let's have an isosceles triangle with a base AC = 6 and the height h = 10         AC/2 * h = 30

A side of a square ( a ):        a / (3 - a / 2) = 10 / 3  

x² + ( x - 6 )² = 260

PB = √22 

Well, this is my answer.

x (x + 9) = 112

In trapezoid PQRS, Base PQ is parallel to base RS. Let point X  be the intersection of diagonals PR and QS. The area of triangle PQX is 20 and the area of triangle RSX is 45 Find the area of trapezoid PQRS.

Since the type of trapezoid is not given, we may use isosceles trapezoid.

Bases are 10 and 18, and the height is 9.