Question

rhombus has area of 4800m² and its side is 100 m and its one diagonal is 160m find its other diagonal

with explaination
I am giving you 50 points please give me accurate answer with solution ​

Answer 1

Answer:

$\bf\underline\red{Quetion:} \\ \\ \: rhombus \: has \: area \: of \: \\ 4800m² \: and \: its \: side \: is \\ \: 100 m \: and \: its \: one \: diagonal \\ \: is \: 160m . \: find \: its \: other \: diagonal \: \\ \\ \large\bf\underline\red{Answer:} \\ \\ We \: know \: in \: a \: rhombus \: \ each \: side \\ \: is \: equal. \: </p><p></p><p>Let \: each \: side \: = \: X cm. \\ \\ </p><p></p><p>We \: have: \: \\ \\ </p><p></p><p> \: 4X \: = \: 1004X \: = \: 100 \\ </p><p></p><p> \: X \: = \: 100 \: / \: 4X \: = \: 100/4 \: \\ </p><p></p><p> \: X \: = \: 25cmX \: = \: 25cm \: \\ </p><p></p><p> \: Now \: let \: one \: of \: the \: diagonal \: be = Y \\ \: cm \: and \: the \: other \: is \: 14 cm(Given). \\ \\ </p><p></p><p>See, \: this \: figure: \: \\ </p><p></p><p> \: AB \: = \: 25cm \: AB \: = \: 25cm \\ </p><p></p><p> \: AO \: = \: AC \: /2 \\ (Diagonal bisecteachother) \\ \: AO=AC \: /2 \: \\ (Diagonal \: bisecteachother) \\ \\ </p><p>AO=14/2=7cm \\ AO=14/2=7cm \\ </p><p></p><p>BO=BD/2BO=BD/2 \\ </p><p></p><p>BO=Y/2cmBO=Y/2cm \\ </p><p></p><p>Intriangle \: AOB \: Intriangle \: AOB \\ </p><p></p><p>Angle \: AOB \: =90 \: Degree \: \\ (Diagonal \: sare \: perpendicular) \: \\ Angle \: AOB=90Degree \: \\ (Diagonalsare \: perpendicular) \\ </p><p></p><p>AO2+BO2=AB2 \: \\ (Pythagoras \: Theorum) \\ AO2+BO2=AB2 \: \\ (Pythagoras \: Theorum) \\ </p><p></p><p>72+(Y/2)2 \\ = 25272+(Y/2)2=252 \\ </p><p></p><p>49+(Y2)/4 \\ =62549+(Y2)/4=625 \\ </p><p></p><p>(Y2)/4 \\ =625–49 \: \\ =576(Y2)/4 \\ \: =625–49=576 \\ </p><p></p><p>Y2=576∗4Y2=576∗4 \\ </p><p></p><p>Y=24∗2Y \\ =24∗2 \\ </p><p></p><p> Y=48cmY =48cm \\ </p><p></p><p>Y/2=24cm \\ </p><p>Now \: we \: know \: area \: of \: Rhombus \: \\ = \: 4*(Area \: of \: triangle \: AOB) \\ </p><p></p><p>Area \: of \: Triangle \: AOB \: \\ =(1/2)∗AO∗BO \: Area \: of \: \\ Triangle \: AOB \\ =(1/2)∗AO∗BO \\ </p><p></p><p>=(1/2)∗24∗7 \\ =(1/2)∗24∗7 \\ </p><p></p><p>=12∗7=12∗7 \\ </p><p></p><p>=84sq.cm=84sq.cm \\ </p><p></p><p>Area \: of \: Rhombus \\ =4∗84 \: Area \: of \: Rhombus \: =4∗84 \\ </p><p></p><p>=336sq.cm=336sq.cm</p><p></p><p>Q.E.D</p><p> \\ \\ </p><p>\large\bf\underline\red{Hope \: it \: helps \: you ❤.}</p><p></p><p>$

Answer 2

Step-by-step explanation:

Area of the rhombus = 4800m²

A=d¹x d²/2

4800m²=160m x d²/2

9600m²=160m x d²

9600m²/160m=d²

60m=d²