Question

One side of rectangular field is 15m and one of it's diagonal is 17m find the area of field

Answer 1

By Pythagoras Theorem we will be able to calculate the other side:
$\sqrt{ {17}^{2} - {15}^{2} } \\ = \sqrt{64} \\ = 8 \: units$
Therefore, the other side of the field is 8m.

Using the area of rectangle formula,
$l \times b$
we get,
$l = 15 \\ b = 8 \\ = l \times b \\ = 15 \times 8 \\ = 120 \: units$
Therefore, the area of rectangular field is:
$120 {m}^{2}$

Answer 2

GIVEN:

• One side of rectangular field is 15m
• diagonal of rectangular field is 17m

TO FIND:

• What is the area of the rectangular field ?

SOLUTION:

Let one side of the rectangular field be 'b'

☞ To find the one side of the rectangular field, we use the Pythagoras theorem

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

• Hypotenuse = 17 m
• Base = b m
• Perpendicular = 15 m

According to question:-

On putting the values in the formula, we get

$\rm{\dashrightarrow (17)^2 = (b)^2 + (15)^2}$

$\rm{\dashrightarrow 289 = b^2 + 225}$

$\rm{\dashrightarrow 289 -225 = b^2}$

$\rm{\dashrightarrow b^2 = 64}$

$\large\bf{\dashrightarrow \star \: b = 8 \: m\: \star }$

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

• Length = 15 m
• Breadth = 8 m

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

On putting the values in the formula, we get

$\rm{\dashrightarrow AREA = 15 \times 8}$

$\large\bf{\dashrightarrow \star \: AREA = 120 \: m^2\: \star }$

❝ Hence, the area of rectangular field is 120 m² ❞

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