Question

One side of a rectangular field is 30 metre and one of its diagonals is 34 metre find the area of the field

Answer 1

$\huge{\underline{\purple{\rm{Solution:}}}}$

$\large{\underline{\red{\rm{let:}}}}$

• $\sf{The\:other\:side\:of\: rectangle=x}$

$\small{\underline{\green{\rm{Given:}}}}$

$\sf{One\:side\:of\:rectangle=30m}$

$\sf{Diagonal\:of\:rectangle=34m}$

$\small{\underline{\orange{\rm{To\: Find:}}}}$

• $\sf{The\:area\:of\: rectangle=?}$

$\small{\underline{\orange{\rm{According\:to\:the\:Question:}}}}$

• $\sf{By\: pathagoras\: theorem}$

$\rm\orange{\boxed{Perpendicular^2+base^2=hypotenous^2}}$

• $\rm{\implies Here\:h=34m\:b=30m\:P=x}$

$\rm{\implies x^2+30^2=34^2}$

$\rm{\implies x^2+900=1156}$

$\rm{\implies x^2=1156-900}$

$\rm{\implies x^2=256}$

$\rm{\implies x=\sqrt{256}}$

$\rm\green{\implies x=-16\:or\:+16}$

• $\sf{Here\:negative\: value\: can't\:be\:kept\:we\:take\:x=16}$

$\rm\green{\implies length=30m}$

$\rm\green{\implies breadth=16m}$

• [Now, Calculate the area]

$\rm{\implies Area\:of\: rectangle=l*b}$

$\rm{\implies Area\:of\: rectangle=30*16}$

$\rm{\implies Area\:of\: rectangle=480\:m^2}$

Hence,

$\rm\purple{\implies Area\:of\: rectangle=480\:m^2}$

Answer 2

GiveN :

• Length (L) = 30 m
• Diagonal = 34 m

To FinD :

• Area of the Field

SolutioN :

Use Pythagoras theorem in Δ ABC, to find the value of breadth. Then put value of breadth and we can find area of field.

$\underbrace{\sf{Breadth \: of \: Rectangular \: field}}$

Use Pythagoras theorem in ΔABC

$\implies \sf{AB^2 \: + \: BC^2 \: = \: CA^2} \\ \\ \implies \sf{AB^2 \: + \: (30)^2 \: = \: (34)^2} \\ \\ \implies \sf{AB^2 \: = \: 34^2 \: - \: 30^2} \\ \\ \implies \sf{AB^2 \: = \: 1156 \: - \: 900} \\ \\ \implies \sf{AB^2 \: = \: 256} \\ \\ \implies \sf{AB \: = \: \sqrt{256}} \\ \\ \implies \sf{AB \: = \: \pm 16}$

As length can't be negative. So, we will take breadth as + 16 m

$\underline{\underline{\sf{Breadth \: of \: Rectangle \: is \: 16 \: m}}}$

______________________________

$\underbrace{\sf{Area \: of \: Rectangular \: Field}}$

$\implies \sf{Area \: = \: length \: \times \: breadth} \\ \\ \implies \sf{Area \: = \: 30 \: \times \: 16} \\ \\ \implies \sf{Area \: = \: 480} \\ \\ \underline{\underline{\sf{Area \: of \: Rectangle \: is \: 480 \: m^2}}}$