Question

The length of a rectangular field is 30m and its diagonal is 34m. Find the breadth of the field and its perimeter

Answer 1

Given :-

length of a rectangular field is 30m

diagonal = 34m

To be found :-

The breadth and perimeter

let breadth be 'b'

$\bf {(breadth)}^{2}+{(length)}^{2}={ (diagonal) }^{2}\\\\={(b)}^{2}+{(30)}^{2} ={(34)}^{2}\\\\={(b)}^{2}+900=1156\\\\={(b)}^{2}=1156-900\\\\={(b)}^{2}=256\\\\=b=\sqrt{256}\\\\=b=16$

breadth = 16 m

perimeter of rectangular field

$\bf = 2(length + breadth) \\\\ =2(30 + 16)\\\\ = 2 \times 46 \\\\= 92$

perimeter = 92 m

Hence,

The breadth is 16 m

and the perimeter is 92 m

Answer 2

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The Measure of shorter side of the Rectangle is 16 m.

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

Diagonal of the Rectangular Garden = 34m

Longer side measures = 30m

To Find :

The Length of the shorter side of the garden.

Solution :

Refer the Attachment for the diagram.

By Pythagoras Theorum -

The Diagonal of the Rectangle is the Hypotenuse.

Measure of the shorter side is the Height.

The longer side (Length) is the Base

In ∆ ACD -

Hypotenuse = 34

Height = x

Base = 30

(Hypotenuse)² = (Base)² + (Height)²

⟶ (34)² = (30)² + (x)²

⟶ 1156 = 900 + x²

⟶ x² = 1156 - 900

⟶ x² = 256

⟶ x = √256

⟶ x = 16

Height = 16 m

∴ The Measure of shorter side of the Rectangle is 16 m.