Question

09.
corner to corne
If the diagonal of a rectangular field is 53 m and its width is 28 m, what is the length of the field?
find the length of the diagonal of a rectangle whose length is 24 cm and width is 7 cm.
and then 65 km due east How far is the chini
(10,​

Answer 1

Appropriate Questions:

❶) If the diagonal of a rectangular field is 53 m and it's width is 28 m, what is the length of the field?

❷) Find the length of the diagonal of a rectangle whose length is 24 cm and width is 7 cm.

AnswEr :

[1]

Given :

• Diagonal of a rectangular field is 53 m.
• Width of the rectangular field = 28 m

To Find :

• The length of the field.

Solution :

So, in order to calculate the length we need to apply Pythagorean theorem,

• (Diagonal)² = (Length)² + (Breadth)²

Substituting values,

$\implies \tt \:(Diagonal)^{2} = (Length)^{2} + (Breadth)^{2} \\ \\ \: \implies \tt \:(53)^{2} = (Length)^{2} + (28)^{2} \\ \\ \implies \tt \: 2809 = (Length)^{2} + 784 \\ \\ \implies \tt \: Length^{2} = 2809 - 784 \\ \\ \implies \tt \: Length = \sqrt{2025} \\ \\ \implies \underline{ \boxed{ \pink{ \tt{Length = 45 \: m}}}}$

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$\therefore \: \underline{ \sf{Length \: of \: the \: field = \bf 45 \: m}}$

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[2]

Given :

• Length of the rectangle = 24 cm
• Breadth of the rectangle = 7 cm

To Find :

• The length of diagonal of a rectangle.

Solution :

So, here we need to apply the formula of Pythagorean theorem,

• (Diagonal)² = (Length)² + (Breadth)²

Substituting values,

$\implies \tt \: (Diagonal)^{2} = (Length)^{2} + (Breadth)^{2} \\ \\ \implies \tt \: (Diagonal)^{2} = (24)^{2} + (7)^{2} \\ \\ \implies \tt \: (Diagonal)^{2} = 576 + 49 \\ \\ \implies \tt \: Diagonal = \sqrt{625} \\ \\ \implies \underline{ \boxed{ \purple{ \tt{Diagonal = 25 \: cm}}}}$

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$\therefore \: \underline{ \sf{Length \: of \: diagonal \: of \: rectangle = \bf 25 \: cm}}$