In the given image if BCDE is a square, then what is the area of the biggest rectangle in
c
m
2
.
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In the given image if BCDE is a square, then what is the area of the biggest rectangle in
c
m
2
.
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Answer:
cm2
Step-by-step explanation:
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Given:
CE = [tex]3\sqrt{2}[/tex] cm
AE = 5cm
To find:
Area of rectangle ACDF.
Formula to be used:
Area of rectangle is length x breadth.
Pythagoras theorem = [tex]H^{2} =P^{2} +B^{2}[/tex]
Step-by-step explanation:
Step 1 of 3
In ΔEBC,
BC = BE
∠EBC=90°, so we can apply pythagoras theorem in this triangle.
[tex](3\sqrt{2} )^{2}=BE^{2} +BC^{2} \\ \\18=BE^{2} +BE^{2} \\\\18=2BE^{2}\\\\9=BE^{2} \\\\BE=3[/tex]
BE = BC = 3cm
Step 2 of 3
Similarly in ΔABE,
[tex]5^{2} =BE^{2} +AB^{2} \\\\25=3^{2} +AB^{2} \\\\AB^{2} =25-9\\\\AB^{2} =16\\\\AB=4cm[/tex]
Step 3 of 3
Sides of rectangle,
BE = CD = 3cm
AC = AB + BC = 4 + 3 = 7cm
Area of rectangle ACDF =
[tex]=AC *CD\\\\=7*3\\\\=21cm^{2}[/tex]
AREA OF RECTANGLE IS 21cm2.