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Area of a quadrilateral ABCD is 20 cm² and perpendiculars on BD from opposite vertices are 1 cm and 1.5 cm. The length of BD is
(a) 4 cm
(b) 15 cm
(c) 16 cm
(d) 18 cm

Solution:

The area of the quadrilateral ABCD can be expressed as the sum of two triangles △ABD and △CBD.

The area of triangles △ABD and △CBD is calculated as:

Let us assume the altitude of △ABD is 1 cm and

Altitude of △ABD is 1.5 cm

The base BD is common to both triangles

Therefore The Area of the quadrilateral(A)

A = (1/2) × (BD) × (1) + (1/2) × (BD) × (1.5)

A = BD/2 + 3BD/4

A = 5BD/4

The area of the quadrilateral is given as 20 cm² , therefore

A = 5BD/4

20 = 5BD/4

BD = 16 cm

The correct choice is therefore ( c ).

✦ Try This: Area of a quadrilateral ABCD is 28cm² and perpendiculars on BD from opposite vertices are 1.5 cm and 2 cm. The length of BD is (a) 8 cm, (b) 12 cm, (c) 16 cm, (d) 6 cm

The area of the quadrilateral ABCD can be expressed as the sum of two triangles △ABD and △CBD.

The area of triangles △ABD and △CBD is calculated as:

Let us assume the altitude of △ABD is 1.5 cm and

Altitude of △ABD is 2 cm

The base BD is common to both triangles

Therefore The Area of the quadrilateral(A)

A = (1/2) × (BD) × (1.5) + (1/2) × (BD) × (2)

A = 3BD/2 + 2B

A = 7BD/2

The area of the quadrilateral is given as 20 cm² , therefore

A = 7BD/2

28 = 7BD/2

BD = 8 cm

The correct choice is therefore (a).

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11

NCERT Exemplar Class 8 Maths Chapter 11 Problem 20

Area of a quadrilateral ABCD is 20 cm² and perpendiculars on BD from opposite vertices are 1 cm and 1.5 cm. The length of BD is (a) 4 cm (b) 15 cm (c) 16 cm (d) 18 cm

Summary:

Area of a quadrilateral ABCD is 20 cm² and perpendiculars on BD from opposite vertices are 1 cm and 1.5 cm. The length of BD is 16 cm

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