If the breadth of rectangle is 10 cm less than the length of rectangle

1.	If the breadth of rectangle is 10 cm less than the length of rectangle and the product of two corresponding sides is 24 cm2, what is the value of breadth of the rectangle? 1. 12 cm2. 2 cm3. 8 cm4. 4 cm
Answer» Correct Answer - Option 2 : 2 cm Given: Breadth (B) of rectangle = Length (L) of rectangle - 10 cm Product of sides = 24 cm² Concepts used: Product of sides = Length × Breadth Calculation: B = L – 10 cm L × B = 24 cm² ⇒ L × (L – 10) = 24 cm² ⇒ L² – 10L = 24 cm² ⇒ L2 – 10L - 24 = 0 ⇒ L² – (12 – 2)L - 24 = 0 ⇒ L²– 12L + 2L – 24 = 0 ⇒ L(L – 12) + 2(L – 12) = 0 ⇒ (L – 12) (L + 2) = 0 ⇒ (L – 12) = 0 or (L + 2) = 0 ⇒ L + 2 = 0 ⇒ L = -2 cm As length (L) cannot be negative, ⇒ L – 12 = 0 ⇒ L = 12 cm. ⇒ B = L – 10 cm ⇒ B = 12 – 10 cm ⇒ B = 2 cm. ∴ The value of the breadth of the rectangle is 2 cm.

If the breadth of rectangle is 10 cm less than the length of rectangle and the product of two corresponding sides is 24 cm2, what is the value of breadth of the rectangle? 1. 12 cm2. 2 cm3. 8 cm4. 4 cm

Answer» Correct Answer - Option 2 : 2 cm

Given:

Breadth (B) of rectangle = Length (L) of rectangle - 10 cm

Product of sides = 24 cm²

Concepts used:

Product of sides = Length × Breadth

Calculation:

B = L – 10 cm

L × B = 24 cm²

⇒ L × (L – 10) = 24 cm²

⇒ L² – 10L = 24 cm²

⇒ L2 – 10L - 24 = 0

⇒ L² – (12 – 2)L - 24 = 0

⇒ L²– 12L + 2L – 24 = 0

⇒ L(L – 12) + 2(L – 12) = 0

⇒ (L – 12) (L + 2) = 0

⇒ (L – 12) = 0 or (L + 2) = 0

⇒ L + 2 = 0

⇒ L = -2 cm

As length (L) cannot be negative,

⇒ L – 12 = 0

⇒ L = 12 cm.

⇒ B = L – 10 cm

⇒ B = 12 – 10 cm

⇒ B = 2 cm.

∴ The value of the breadth of the rectangle is 2 cm.

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