Question

. 12. The diagonal of a square plotis 42m. Find () its area and (1) the length of each side "The diagonals of a rhombus are 18 cm and 24 cm. Find (0) its area and the length​

Answer 1

Answer:

Diagonal of rhombus are 18 cm and 24 cm.

area of rhombus = 1/2 x Product of diagonals

= 1/2 x 18 x 24

= 216 cm2

(ii) Diagonals of rhombus bisect each other at right angles.

∴ OA = (1/2) × 24 = 12 cm

OB = (1/2) × 18 = 9 cm

In right ∠d ∆ AOB

∴ Side of rhombus = 15 cm

(iii) Perimeter of rhombus = 4 × side

= 4 × 15 = 60 cm

(i) 216 cm2 (ii) 15 cm (iii) 60 cm

Answer 2

Answer:

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Step-by-step explanation:

$Q.1 \\ so \: here \: diagonal \: of \: square = 42.m \\ so \: we \: know \: that \: \\ diagonal \: of \: square = \sqrt{2} \times side \: of \: square \\ ie \: side \: of \: square = \frac{42}{ \sqrt{2} } \\ \\ = \frac{42}{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } \\ \\ = \frac{42 \sqrt{2} }{( \sqrt{2} ) {}^{2} } \\ \\ = \frac{42 \sqrt{2} }{2} \\ \\ = 21. \sqrt{2} \\ hence \: side \: of \: square = 21. \sqrt{2} \: m$

$now \: so \: we \: know \: that \\ area \: of \: square = side {}^{2} \\ = (21 \sqrt{2} ) {}^{2} \\ = 21 \times 21 \times 2 \\ = 441 \times 2 \\ = 882.m {}^{2}$

$Q.2 \\ so \: here \: diagonals \: of \: rhombus \: are \: 18.cm \: \: and \: \: 24.cm \\ so \: let \: \: d1 = 18.cm \\ d2 = 24.cm \\ \\ we \: know \: that \\ area \: of \: rhombus = \frac{1}{2} \times d1 \times d2 \\ \\ = \frac{1}{2} \times 18 \times 24 \\ \\ = 9 \times 24 \\ = 216. \: cm {}^{2}$