Question

4. One side of a rectangular field is 15 m and one of
its diagonal is 17 m. Find the area of a field.​

Answer 1

Answer:

Area of the field = 120 m².

Step-by-step explanation:

• One side of the rectangular field = 15 m
• One of its diagonal = 17 m

Now find the other side of the rectangular field by using ' Pythagoras Theorem '.

From the attachment :

• AD= length = 15 m
• AC = Diagonal = 17 m

DC² + AD² = AC²

→ DC² + 15² = 17²

→ DC² = 17² - 15²

→ DC² = 64

→ DC = √64

→ DC = 8

Therefore, breadth of the rectangular field is 8 m.

We know that,

${\boxed{\large{\sf{Area\:of\: rectangle=length\times\: breadth}}}}$

→ Area of the field = (15×8) m²

→ Area of the field = 120 m²

_____________________

More info:

• Perimeter of rectangle = 2(length× breadth)
• Diagonal of rectangle = √(length ²+breadth ²)
• Area of square = side²
• Perimeter of square = 4× side

Answer 2

Answer:

Given :-

• One side of a rectangular field is 15 m and one of its diagonal is 17 m.

To Find :-

• What is the area of a field.

Formula Used :-

$\bigstar \: \boxed{\sf{Area\: of\: Rectangle =\: Length \times Breadth}}$

Solution :-

Given :

• One side of a rectangular field = 15 m.
• Diagonal of a rectangular field = 17 m

Let, the length BC be 15 m

And, the diagonal AC be 17 m

Then, according to the Pythagoras theorem we know that,

↦ $\sf {(AB)}^{2} =\: {(AC)}^{2} - {(BC)}^{2}$

↦ $\sf {(AB)}^{2} =\: {(17)}^{2} - {(15)}^{2}$

↦ $\sf {(AB)}^{2} =\: 289 - 225$

↦ $\sf {(AB)}^{2} =\: 64$

↦ $\sf AB =\: \sqrt{64}$

➦ $\sf\bold{\pink{AB =\: 8\: m}}$

Hence, the breadth of a rectangular field is 8 m.

Now, we have to find the area of a rectangular field,

Given :

• Length of a rectangular field = 15 m
• Breadth of a rectangular field = 8 m

According to the question by using the formula we get,

$\sf \implies Area\: of\: rectangular\: field =\: 15\: m \times 8\: m$

$\sf \implies \bold{\red{Area\: of\: rectangular\: field =\: 120\: {m}^{2}}}$

$\therefore$ The area of a rectangular field is 120 m² .