1. Find the area of a rectangular field, one side of which is 48 metres and its diagonal is 50 metres
Answers
Given :
- Diagonal of the field = 50 m
- Length or one side of the field = 48 m
To Find :
The area of the rectangular field.
Solution :
Analysis :
Here to find the area we need both the length and breadth of the rectangle. We are given the diagonal and the length. So from the diagonal formula we can get the breadth of the rectangle. And from that we can find the area.
Required Formula :
- Diagonal = √[l² + b²]
- Area of rectangle = Length × Breadth
where,
- l = Length
- b = Breadth
Explanation :
The breadth :
Let us assume that the breadth is “b” m.
We know that if we are diagonal of the rectangle and the length and is asked to find the breadth of the rectangle then our required formula is,
Diagonal = √[l² + b²]
where,
- Diagonal = 50 m
- l = 48 m
- b = b m
Using the required formula and substituting the required values,
⇒ Diagonal = √[l² + b²]
⇒ 50 = √[(48)² + b²]
Squaring both the sides,
⇒ (50)² = (48)² + b²
⇒ 2500 = 2304 + b²
⇒ 2500 - 2304 = b²
⇒ 196 = b²
Square rooting both the sides,
⇒ √196 = b
⇒ √[14 × 14] = b
⇒ 14 = b
∴ Breadth = 14 m.
Area :
We know that if we are given the length and breadth of the rectangle then our required formula is,
Area of rectangle = Length × Breadth
where,
- Length = 48 m
- Breadth = 14 m
Using the required formula and substituting the required values,
⇒ Area = Length × Breadth
⇒ Area = 48 × 14
⇒ Area = 672
∴ Area = 672 m².
Area of the rectangular field is 672 m².
Answer:
672 m²
Step-by-step explanation:
we divided the rectangle in two triangles and found the other side
by Pythagoras theorem
H²=B²+P²
(50)²=x²+(48)²
2500=x²+2304
x²=2500-2304
x²=196
x=√196
x=14m
now the b=14m and length=48m
area of rectangle= length × breadth
48×14=672m²
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