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The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.

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CBSE/Class 10/Mathematics/UNIT II: Algebra/Quadratic Equations/NCERT Solutions/Exercise 4.3

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Smaller side__90m Larger side__120m
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Professional Structural Designer

(x+30)+x= (x+60) x+60x+900+x2=x2+3600+120x x=(60120)/2 x=90 short side = 90m long side =120m diagonal=150m read more

(x+30)+x= (x+60)

x+60x+900+x2=x2+3600+120x

x=(60120)/2

x=90

short side = 90m

long side =120m

diagonal=150m

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Comments

Tutor

Sides are 90 m and 120m
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Teacher

90 &120 meters
Comments

Tutor

Let shorter side be x Diagonal = x+60 Longer side =x+30 By applying Pythagoras theorem Shorter side = 90m Longer side =120m
Comments

Tutor

Smaller Side = 90m Larger Side = 120m Diagonal = 150m
Comments

Let the shorter side be x. Therefore, the diagonal = x + 60 & the longer side = x + 30. Using the Pythagoras theorem, x² + (x + 30)² = (x + 60)² or x² + x² + 60x + 900 = x² + 120x + 3600 or x² - 60x - 2700 = 0 or x² - 90x + 30x - 2700 = 0 or x(x - 90) + 30(x... read more

Let the shorter side be x. Therefore, the diagonal = x + 60 & the longer side = x + 30.

Using the Pythagoras theorem, 

x² + (x + 30)² = (x + 60)² 

or x² + x² + 60x + 900 = x² + 120x + 3600

or x² - 60x - 2700 = 0

or x² - 90x + 30x - 2700 = 0

or x(x - 90) + 30(x - 90) = 0

or (x - 90) (x + 30) = 0

x = 90 or x = - 30

Since length can't be negative, therefore, the shorter side is 90m & the longer side is 120m.

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The smaller side is 90. The longer side is 120.
Comments

Tutor

The longest side of the triangles i.e. the hypotenuse.So, by Pythagoras Theorem,(Diagonal)² = (Smaller Side)² + (Longer Side)²(x + 60)² = (x)² + (x + 30)²x² + 120x + 3600 = x² + x² + 60x + 900x² + 60x - 120x + 900 - 3600 = 0x² - 60x - 2700 = 0x²... read more

The longest side of the triangles i.e. the hypotenuse.
So, by Pythagoras Theorem,
(Diagonal)² = (Smaller Side)² + (Longer Side)²
(x + 60)² = (x)² + (x + 30)²
x² + 120x + 3600 = x² + x² + 60x + 900
x² + 60x - 120x + 900 - 3600 = 0
x² - 60x - 2700 = 0
x² - 90x + 30x - 2700 = 0
x(x - 90) + 30(x - 90) = 0
(x - 90) (x + 30) = 0
x = 90 because x = -30 as length cannot be possible.
So the length of the shorter side is 90 meters and the length of the longer side is 90 + 30 = 120 meters.

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Tutor

Let the length of the shorter side be x metres. The length of the diagonal= 60+x metres The length of the longer side =30+x metres Applying Pythagoras theorem, Diagonal²=longer side²+shorter side² (60+x) ²= (30+x) ² + x² 3600+120x+x²=900+60x+x²+x² 2700+60x-x²=0 2700+90x-30x-x²=0 90(30+x)-x(30+x)... read more

Let the length of the shorter side be x metres. 

The length of the diagonal= 60+x metres

The length of the longer side =30+x metres

Applying Pythagoras theorem, 

Diagonal²=longer side²+shorter side²

(60+x) ²= (30+x) ² + x²

3600+120x+x²=900+60x+x²+x²

2700+60x-x²=0

2700+90x-30x-x²=0

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

X=90, 

Shorter side is 90m,  longer side is 90+30=120m

 

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