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The diagonal and one side of a rectangular field are 100 m and 80 m, respectively. What is the area of the rectangular field?
4800 square meters
5000 square meters
4200 square meters
8000 square meters
4800 square meters
Recognize the 3-4-5 Pythagorean triplet scaled by 20: 3(20)=60, 4(20)=80, 5(20)=100. Thus, the missing side is 60m, and the area is 60 * 80 = 4800.
Diagonal (d) = 100 m, one side (a) = 80 m of a rectangular field.
d2=a2+b2, Area=a├Чb
Recognize the 3-4-5 Pythagorean triplet scaled by 20: 3(20)=60, 4(20)=80, 5(20)=100. Thus, the missing side is 60m, and the area is 60 * 80 = 4800.
Students often mistake the diagonal for another side or try to use the area formula L├ЧB without calculating the second side B first using Pythagoras.
Identify the relationship
In a rectangle, the diagonal divides it into two right-angled triangles. We use the Pythagorean theorem where d2=a2+b2.
1002=802+b2
Calculate the missing side
Subtract the square of the known side from the square of the diagonal: b2=10000тИТ6400=3600. Thus, b=3600тАЛ.
b=60┬аm
Calculate the area
Apply the area formula for a rectangle: Area=length├Чbreadth.
Area=80├Ч60=4800┬аsquare┬аmeters
A is correct because the sides are 80 m and 60 m, resulting in an area of 4800 square meters.
This concept of identifying Pythagorean triplets is essential in Coordinate Geometry for finding distances and in Trigonometry for determining ratio values.
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