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Mathematics

Assertion (A) : The diagonal of a rectangle is 17 m and its breadth is 8 m. Half of the area of rectangle is 120 m2.

Reason (R) : The diagonal of every rectangle, divide into two congruent right-triangles.

  1. Both A and R are correct, and R is the correct explanation for A.

  2. Both A and R are correct, and R is not the correct explanation for A.

  3. A is true, but R is false.

  4. A is false, but R is true.

Area Trapezium Polygon

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Answer

Given,

The diagonal of the rectangle = 17 m

The breadth of the rectangle = 8 m

Using Pythagoras theorem in rectangle,

⇒ Diagonal2 = Length2 + Breadth2

⇒ 172 = l2 + 82

⇒ 289 = l2 + 64

⇒ l2 = 289 - 64

⇒ l2 = 225

⇒ l = 225\sqrt{225}

⇒ l = 15 m.

By formula,

Area of rectangle = l x b = 15 x 8 = 120 m2.

Half of the area of rectangle = 1202\dfrac{120}{2} = 60 m2.

So, assertion (A) is false.

ABCD is a rectangle. BD is a diagonal.

Assertion: The diagonal of a rectangle is 17 m and its breadth is 8 m. Half of the area of rectangle is 120 m. Reason: The diagonal of every rectangle, divide into two congruent right-triangles. Area of a Trapezium and a Polygon, Concise Mathematics Solutions ICSE Class 8.

In Δ ABD and Δ BDC,

⇒ AB = DC (Opposite sides of rectangle are equal)

⇒ AD = BC (Opposite sides of rectangle are equal)

⇒ BD = BD (Common)

∴ Δ ABD ≅ Δ BDC (By SSS congruency criterion)

Thus the diagonal of every rectangle, divide into two congruent right-triangles.

So, reason (R) is true.

∴ A is false, but R is true.

Hence, option 4 is the correct option.

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