Question

if two diagonals of a rhombous are of length 90m and 400m then find the height and perimeter of the rhombous
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Answer 1

Question:

if two diagonals of a rhombous are of length 90m and 400m then find the height and perimeter of the rhombous

Answer:

820m

Step-by-step explanation:

Let the Rhombus be ABCD

We know that :

$\pink {diagonals \ of \ rhombus \ are \ perpendicular \ bisector \ of \ each\ other.}$

${\bold {\pink{GIVEN}}}$

Diagonal = A.C. = 90cm

Diagonal = BD = 400 cm

${ AO = OC = 90/2 = 45cm}$

${BO = OD = 400/2 = 200cm}$

Triangle DOC is an right angles triangle

(DC)^2 = (OD)^2 + (OD)^2 [pythagorus]

(DC)^2 = (200)^2 + (45)^2

(DC)^2 = (40,000) + (2,025)

(DC)^2 = 42,025

(DC) = root (42,025)

(DC) = 205cm

Perimeter = 205 × 4

Perimeter = 820m

Answer 2

$\large\bf\underline{Given:-}$

• Diagonals of rhombus = 90m and 400m

$\large\bf\underline {To \: find:-}$

• Height
• perimeter

$\huge\bf\underline{Solution:-}$

Formula for finding the side of rhombus when diagonals are given.

$\large \dag \: \bf \: side = \frac{ \sqrt{(diagonal1) {}^{2} + {(diagonal2)}^{2} } }{2}$

$\dashrightarrow \rm \: side = \frac{ \sqrt{ {90}^{2} + {400}^{2} }}{2} \\ \\ \dashrightarrow \rm \: side = \frac{ \sqrt{8100 + 160000} }{2} \\ \\ \dashrightarrow \rm \: side = \frac{ \sqrt{168100} }{2} \\ \\ \dashrightarrow \rm \: side = \frac{410}{2} \\ \\ \dashrightarrow \rm \: side = 205$

Area of rhombus when diagonals are given:-

$\large \bf \dag \: \: area = \frac{1}{2} \times d_ 1 \times d_2 \: sq.units$

$\rightarrowtail \rm \: \frac{1}{2} \times 90 \times 400 \\ \\ \rightarrowtail \rm \: \frac{1}{2} \times 36000 \\ \\ \rightarrowtail \rm \: \cancel\frac{36000}{2} \\ \\ \rightarrowtail \rm \: 18000 \: sq.units$

Area of rhombus = 18000

• base = 205 m

$\longrightarrow \rm \: b \times h = 18000 \\ \\ \longrightarrow \rm \: 205 \times h = 18000 \\ \\ \longrightarrow \rm \: h = \frac{18000}{205} \\ \\ \longrightarrow \bf \: h = 87.8m$

Perimeter of rhombus :-

$\large \bf \dag \: \: perimeter = 4 \times (side)$

$\longmapsto \rm \: perimeter = \: 4 \times 205 \\ \\ \longmapsto \rm \: perimeter = 820 \: units$

So,

★ Height of rhombus = 87.8m

✦ Perimeter of rhombus = 820m