MATH SOLVE

2 months ago

Q:
# In the figure below , ABCD is a square . Points are chosen on each pair of adjacent sides of ABCD to form 4 congruent right triangles as shown below . Each of these has one leg that is twice as long as the other leg what fraction of the area of square ABCD is shaded

Accepted Solution

A:

Answer:5/9 of the area of square ABCD is shadedStep-by-step explanation:see the attached figure to better understand the problemwe know thatTo find out what fraction of the area of square ABCD is shaded, divide the shaded area by the total area of square ABCDstep 1Find out the area of square ABCDThe area of a square is[tex]A=b^{2}[/tex]whereb is the length side of the squarewe have[tex]b=(x+2x)=3x\ units[/tex]so[tex]A=(3x)^{2}[/tex][tex]A=9x^2\ units^{2}[/tex]step 2Find out the area of the 4 congruent right triangles[tex]A=4[\frac{1}{2}(x)(2x)]=4x^{2}\ units^2[/tex]step 3Find out the area of the shaded regionThe area of the shaded region is equal to the area of square ABCD minus the area of the 4 congruent right trianglesso[tex]A=9x^2-4x^{2}=5x^{2}\ units^{2}[/tex]step 4Divide the shaded area by the total area of square ABCD[tex]\frac{5x^{2}}{9x^{2}} =\frac{5}{9}[/tex]therefore5/9 of the area of square ABCD is shaded