maths
posted by Candice .
Let ABCD be a square with side legnth 7cm. Another square KLMN is inscribed into ABCD such that its vertices lie on the sides of ABCD.
Find the lenghts of parts of ABCD sides which are divided by the vertices of KLMN. If [the area of KLMN]: [area of ABCD] = 25:49

you will have 4 congruent triangles.
each will have legs of x and 7x and a hypotenuse of 5
thus x^2 + (7x)^2 = 25
solve as a quadratic, it factors nicely, and you should have sides of 3 and 4 
How would you know that the hypotenuse is length 5? Does it have something to do with the ratio?
Respond to this Question
Similar Questions

geometry
quadrilateral ABCD has right angles at B and D. If ABCD is kiteshaped with AB=AD=20 and BC=CD=15, find the radius of the circle inscribed in ABCD. 
Geometry
Circle O is inscribed is square ABCD, and at the same time, is circumscribed about square PQRS. WHich are is the smaller area, the region inside the inscribed circle minus the area of square PQRS or the are inside square ABCD minus … 
GEOmetry!!.....
ABCD is a trapezoid with AB<CD and AB parallel to CD. Γ is a circle inscribed in ABCD, such that Γ is tangent to all four sides. If AD=BC=25 and the area of ABCD is 600, what is the radius of Γ? 
Geometry
ABCD is a trapezoid with AB < CD and AB parallel to CD. \Gamma is a circle inscribed in ABCD, such that \Gamma is tangent to all four sides. If AD = BC = 25 and the area of ABCD is 600, what is the radius of \Gamma? 
hellllllllllllllp maaaath
ABCD is a square. P is a point within ABCD such that PA=1,PB=29 and PC=41. What is area of square ABCD ? 
math
ABCD is a square. Γ1 is a circle that circumscribes ABCD (i.e. Γ1 passes through points A,B,C and D). Γ2 is a circle that is inscribed in ABCD (i.e. Γ2 is tangential to sides AB,BC,CD and DA). If the area of Γ1 … 
math
ABCD is a square. Γ1 is a circle that circumscribes ABCD (i.e. Γ1 passes through points A,B,C and D). Γ2 is a circle that is inscribed in ABCD (i.e. Γ2 is tangential to sides AB,BC,CD and DA). If the area of Γ1 … 
maths
ABCD is a trapezoid with parallel sides AB and CD. Γ is an inscribed circle of ABCD, and tangential to sides AB,BC,CD and AD at the points E,F,G and H respectively. If AE=2,BE=3, and the radius of Γ is 12, what is the length … 
geometry
A quadrilateral has vertices A(3, 5), B(2, 0), C(7, 0), and D(8, 5). Which statement about the quadrilateral is true? 
Geometry
Points X, Y, and Z are on sides AB, BC, and CD, respectively, of square ABCD. Let O be the intersection of the diagonals of ABCD. Segments XO , YO, and ZO divide the square into three parts with equal areas. If Y is the midpoint of …