Question

In the figure X is the mid point of DC.. ΔAXB is an equilateral triangleand ABCD is a rectangle also DX = 7 cma) What is the measure of∠ AXB?b) What is the measure of∠ DAX ?c) Calculate the area of the rectangle.​

Answer 1

Step-by-step explanation:

$\setlength{\unitlength}{1cm}\begin{picture}(20,15)\thicklines\put(0,0){\line (1,3){1}}\put (4,0){\line (-1,0){4}}\put (4,0){\line (1,3){1}}\put (1,3){\line (1,0){4}}\put (0,0){\line (5,3){5}}\put (4,0){\line(-1,3){0.66}}\put (1,3){\line (1,-3){0.66}}\put (0.5,3){\sf A}\put (1.6,0.7){\sf F}\put (3,2){\sf E}\put(5.1,3){\sf D}\put (4,-0.5){\sf C}\put (0,-0.5){\sf B}\end{picture}$

Answer 2

Answer:

Given, ABC is an equilateral triangle.D, E, F are mid points of the sides of the triangle.

Since, D is mid point of AB and E is mid point of AC, by mid point theorem,

DE=

2

1

AC........(1)

Since, F is mid point of BC and E is mid point of AC, by mid point theorem,

EF=

2

1

AB.........(2)

And we know, BE=

2

1

AB and BF=

2

1

BC.........(3)

Now, from (1), (2) and (3)

Since, all the sides of equilateral triangle are equal,

DE=EF=BE=BF

Hence, BEFD is a rhombus.