Question

Solve the following questions. (4 x 2 = 8 marks) 5) Find the length of the diagonal d if the area of the quadrilateral shown below is 120 cm² and the perpendicular lengths (p, and p₂) measure 5 cm and 7 cm, respectively.​

Answer 1

Answer :—

The Length of The Diagonal of The Quadrilateral is 20cm

Given :—

• Area of Quadrilateral $\longmapsto\tt\bf$ 120 cm²

• Perpendicular lengths $\longmapsto\tt\bf$ 5 cm (h1) and 7 cm (h2)

To Find :—

$\longmapsto\tt\bf$ Length of Diagonal .

Formula Used :—

$\longmapsto\frac{1}{2} \times \: d \: (h1 \: + \: h2)$

Solution :—

$\longmapsto120 \: = \: \frac{1}{2} \times \: d \: (5 \: + \: 7) \\ \\\longmapsto 120 \: \times 2 = \: \: d \: (12) \\ \\ \longmapsto240 \: = \: d(12) \\ \\ \longmapsto \frac{240}{12} = \: d \\ \\\longmapsto d \: = \: 20$

Hence , The Length of The Diagonal of The Quadrilateral is 20cm .