Question

The diagonals of a rhombus are 30cm and 16cm. Find its area, the length of a side and its perimeter.​

Answer 1

Explanation:

`\large \boldsymbol {} \tt Formulas : \\\\d_1^2+d_2^2=4a^2 \\\\S=(1)/(2) d_1d_2 \\\\ \ where \ S \ is \ the \ area \ of \ the \ rhombus \ ;\\\\\ and \ d_1 \ and \ d_2 \ are \ its \ diagonals \ ; \ and \ a \ , \\\\\\ respectively, \ is\ the \ side \ of\ the rhombus \\\\ then : \\\\ 4a^2=16^2+30^2 \\\\ 4a^2=1156 \\\\a^2=289 \\\\a=17 \ \ then \ P=4a=17*4=\boldsymbol {68} \\\\ \tt S=(1)/(2) \cdot 30 \cdot 16 =\boldsymbol {240 } \\\\ Answer : S=240 \ ; a=17 \ ; \ P=68 \ ;`

Answer 2

Area = 1/2 × product of diagonalsso area = 1/2 × 30 ×16 = 240 cm²

also diagonals bisect each other at right angles so 1/2×30= 15cm,, 1/2× 16 = 8cm

therefore by pythagoras theorem,

`{15 }^(2)`+
`{8}^(2)`=
`{side}^(2)`
`√(289 = side)`

side = 17

Perimeter = 4×17 =68 cm.