Question

The diagonal of a rectangular field is 60m more than its breadth.If its length is 30m more than its breadth.find its length and breadth​

Answer 1

Answer:

Let length of shorter side = x m

length of bigger side = (x + 30) m

length of diagonal = (x + 60) m

we have to use Pythagoras theorem,

so, diagonal ² = bigger side² + shorter side²

=> (x + 60)² = (x + 30)² + x²

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

=> 60x + 2700x = x²

=> x² - 60x - 2700 = 0

=> x² - 90x + 30x - 2700 = 0

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

=> x = -30 and 90 but x ≠ -30

hence, length of shorter side = 90m

length of bigger side = 120m

Answer 2

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Given:

The diagonal of a rectangular field is 60m more than its breadth.If its length is 30m more than its breadth.

To find:

Its length and breadth of rectangular field.

Explanation:

• Let the breadth of rectangular field be R

• Let the length of rectangular field be R+30

• Let the diagonal of rectangular field be R + 60

Using Pythagoras Theorem:

[Hypotenuse]² = [base]² + [perpendicular]²

→ [Diagonal]² = [breadth]² + [length]²

→ (R + 60)² = (R)² + (R+30)²

[(a+b)² = a² + b² +2ab]

→ R² + 60² +2× R× 60 = R² + R² +30² + 2× R× 30

→ R² + 3600 + 120R = R² + R² + 900 + 60R

→ R² -R² + 120R -60R +3600 -900 = R²

→ 0 + 60R + 2700 =R²

→ R² -60R - 2700 = 0

[Factorization]

→ R² -90R +30R -2700= 0

→ R(R -90)+30(R -90) = 0

→ (R-90)(R+30) = 0

→ R -90=0  or  R +30= 0

→ R = 90   or   R= -30

Here, two value get, we know that negative value is not acceptable.

∴ R = 90m.

Thus,

• The breadth of the rectangular field = 90m

• The length of the rectangular field is (90+ 30)m =120m.