Question

The diagonal of a rectangular field is 60cm more than the shorter side. if the longer side is 30m more than the shorter side find the sides of the field.​

Answer 1

Answer:

Assume the rectangular field BC = m meters

★Then

AC = (m + 60)

★Then

AB = (m + 30)

AC² = BC² + AB²

(m + 60)² = m² + (m + 30)²

m² + 120m + 3600 = m² + m² + 60m + 900

m² - 60m - 2700 = 0

★Factorise the middle term of LHS we get :-

m² - 90m + 30m - 2700 = 0

m(m - 90) + 30(m - 900) = 0

(m + 30)(m - 90) = 0

m + 30 = 0

m = -30

m - 90 = 0

m = 90

●Sides of rectangle can't be in negative

★Hence :-

●Sides of filled are 120m and 90

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Answer 2

${ \huge{ \boxed{ \bf{\underline{ \red{Answer}}}}}} : -$

The field is rectangular 

Diagonal of a rectangular field is 60 meters more than the shorter side.

Longer side is 30 meters more than the shorter side.

Assume DB as the diagonal of the rectangle ABCD.

Assume AD as the shorter side and name it as ‘x’ 

Consider figure 1,

$\begin{array}{l} \text { Longer side } \mathrm{AB}=x+30 \\ \text { Diaqonal } \mathrm{DB}=x+60 \end{array}$

Take the Right ∆ADB

By Pythagoras Theorem,

$\begin{aligned} D B^{2} &=A B^{2}+A D^{2} \\ (x+60)^{2} &=(x+30)^{2}+x^{2} \\ x^{2}+120 x+3600 &=x^{2}+60 x+900+x^{2} \\ x^{2}-60 x-2700 &=0 \end{aligned}</p><p>$

Evaluate the value of x from (1)

$\begin{aligned} x{2}-60 x-2700 &=0 \\ x{2}-90 x+30 x-2700 &=0 \\ x(x-90)+30(x-90) &=0 \\ (x+30)(x-90) &=0 \\ x=&-30,90 \end{aligned}$

Since distance cannot be negative,

Value of x = 90m

Evaluate the value of longer side AB.

$</p><p>\begin{aligned} A B &=x+30 \\ &=90+30 \\ &=120 m \end{aligned}$

$\pink{\boxed{The\: Answer \:Is :-}}$

Longer Side of Field = 120m.

Shorter Side of Field = 90m

______________________

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