Question

1. Find the area of a rectangular field, one side of which is 48 metres and its diagonal is 50 metres​

Answer 1

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 2

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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