Question

the breadth of a rectangular field is 9 metre its diagonal is 15 metre long what will be the area of rectangular field​

Answer 1

✬ Area = 108 m² ✬

Step-by-step explanation:

Given:

• Measure of breadth of rectangular field is 9m.
• Measure of diagonal of rectangular field is 15m.

To Find:

• What is area of rectangular field ?

Solution: Let ABCD be a rectangular field where,

• AB = DC = Length
• BC = AD = Breadth = 9 m
• AC = Diagonal = 15 m

As we know that the measure of each angle of a rectangle is of 90°. Therefore,

➨ ∠ABC = 90°.

Now, In right angled triangle ABC , we have

• BC = 9 m ( Perpendicular )
• AB = Base
• AC = 15 m ( Hypotenuse )

Applying Pythagoras Theorem in ∆ABC,

★ Pythagoras Theorem: Hypotenuse² = Base² + Perpendicular² ★

$\implies{\rm }$ AC² = AB² + BC²

$\implies{\rm }$ 15² = AB² + 9²

$\implies{\rm }$ 225 = AB² + 81

$\implies{\rm }$ 225 – 81 = AB²

$\implies{\rm }$ 144 = AB²

$\implies{\rm }$ √144 = AB

$\implies{\rm }$ 12 m = AB

So , AB = Length = 12 m & BC = Breadth = 9 m.

★ Area of Rectangle = (Length $\times$ Breadth) ★

$\implies{\rm }$ Area of ABCD = (AB $\times$ BC) m²

$\implies{\rm }$ (12 $\times$ 9) m²

$\implies{\rm }$ 108 m²

Hence, the area of rectangular field is 108 m².

Answer 2

GIVEN:

• Breadth of the rectangular field = 9 m
• Diagonal of rectangular field = 15 m

TO FIND:

• What is the area of the rectangular field ?

SOLUTION:

Let the length of the rectangular field be 'L' m

To find the length of the rectangular field, we use Pythagoras theorem

$\bf{\star \: (Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2 \: \star}$

• Hypotenuse = 15 m
• Base = 9 m
• Length = 'L' m

According to question:-

$\sf{\longrightarrow (15)^2 = (9)^2 +L^2}$

$\sf{\longrightarrow 225 = 81 +L^2}$

$\sf{\longrightarrow 225 - 81 = L^2}$

$\sf{\longrightarrow 144 = L^2}$

$\sf{\longrightarrow \sqrt{144} = L}$

$\bf{\longrightarrow \star \: 12 \: m = L \: \star}$

❝ The length of the rectangular field is 12 m ❞

We know that the formula for finding the area of the rectangular field is:-

$\bf{\star \: Area = Length \times Breadth \: \star}$

According to question:-

$\sf{\longrightarrow Area = 12 \times 9}$

$\bf{\longrightarrow \star \: Area = 108 \: m^2\: \star}$

❝ Hence, the area of the rectangular field is 108 m² ❞

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