Question

The area of a rhombus is 119 m sq and perimeter 56 cm .find its height​

Answer 1

Answer:

area of rhombus = 119

all sides are equal in rhombus

therefore length of side= 56/4= 14

rhombus is a king of parallelogram

therefore area of rhombus = 1/2×b×h

119=1/2×14×h

119=7h

h=119/7

h=17

Answer 2

${\large{\purple{❥}}}$${\large{\underline{\red{\sf{Formula:}}}}}$

${\boxed{\purple{\sf{Area=\frac{D_{1}.D_{2}}{2}}}}}$

${\bold{\sf{D_{1},D_{2} \:are\:diagonals.}}}$

${\boxed{\blue{\sf{Perimater=4a}}}}$

${\bold{\sf{‘a’\:is\:the\:side\:of\:rhombus.}}}$

${\large{\purple{❥}}}$${\large{\underline{\red{\sf{Answer:}}}}}$

${\boxed{\blue{\sf{Perimater=4a=56cm}}}}$

${\boxed{\blue{\sf{a=\frac{56}{4} = 14cm}}}}$

${\boxed{\sf{(\frac{D_{1}}{2})²+(\frac{D_{2}}{2})²=a²}}}$

${\boxed{\sf{\frac{D_{1}²}{4}+\frac{D_{2}²}{4}=(14)²}}}$

${\boxed{\sf{D_{1}²+D_{2}²=784}}}$

${\boxed{\purple{\sf{Area=\frac{D_{1}.D_{2}}{2}=119cm²}}}}$

${\boxed{\purple{\sf{D_{1}.D_{2}=238cm²}}}}$

${\boxed{\sf{(D_{1}+D_{2})²=D_{1}²+D_{2}²+2D_{1}.D_{2}}}}$

${\boxed{\sf{(D_{1}+D_{2})²=784+2(238)}}}$

${\boxed{\sf{D_{1}+D_{2}=\sqrt{1260}=35.5}}}$${\bold{→(i)}}$

${\boxed{\sf{(D_{1}-D_{2})²=D_{1}²+D_{2}²-2D_{1}.D_{2}}}}$

${\boxed{\sf{(D_{1}-D_{2})²=784-2(238)}}}$

${\boxed{\sf{D_{1}-D_{2}=\sqrt{308}=17.5}}}$${\bold{→(ii)}}$

${\bold{(i)+(ii)}}$

${\boxed{\sf{2D_{1}=35.5+17.5=53}}}$

${\boxed{\red{\sf{D_{1}=26.5}}}}$

${\boxed{\sf{D_{2}=35.5-D_{1}=35.5-26.5}}}$

${\boxed{\red{\sf{D_{2}=9}}}}$