The perimeter of △CDE is 55 cm. A rhombus DMFN is inscribed in this triangle so that vertices M, F, and N lie on the sides CD ,
2 answers:
Answer:
CD=20 cm and DE=15 cm. CD=20 cm and DE=15 cm.
Step-by-step explanation:
A rhombus DMFN is inscribed in such a way that it is inscribed in triangle CDE with the vertices M, F, and N l on the sides CD , CE , and DE respectively.
Now, in rhombus, the parallel sides are always parallel, therefore
MF║DE, thus, by the basic proportionality condition.
It is given that CF=8 cm and EF=12 cm, therefore, .
That is CM=8 cm and MD=12 cm. Therefore, CD=CM+MD=8+12=20.
According to question, Perimeter of △CDE =55 cm
⇒CD+DE+CE=55
⇒20+DE+20=55
⇒DE=15 cm
Hence, CD=20 cm and DE=15 cm.
You might be interested in
The answer is: " 17.35 " .
__________________________________
→ The circumference of the circle is: " 17.35 units " .
__________________________________
The area, "A", of a circle:
A = * r² ;
Note: .
The area of the circumference, "C", of a circle:
C = 2 r .
__________________________________________
Given:
A = 24 ;
Use the formula for the area, "A" of a circle, to find the radius, "r" .
Then, plug the value obtained for "r" into the formula for the circumference, "C" , of a circle:
C = 2 r l
To solve for the circumference, "C", of the circle.
________________
A = ;
24 = 3.14 * r² ;
↔ 3.14 * r² = 24 ;
Divide each side of the equation by "(3.14)" ;
[3.14 * r²] / 3.14 = (24) / (3.14) ;
to get:
→ r² = 7.64331210191 ;
Take the positive square root of each side of the equation;
to isolate "r" on one side of the equation; & to solve for the radius, "r" ;
→ ⁺√(r²) = ⁺√(7.64331210191) ;
to get:
→ r = 2.76281034802 ;
____________________________
Now, plug this "obtained value" for the radius, "r" into the equation for the formula for the circumference, "C" of a circle:
→ C = 2 * r ;
to solve for the circumference, "C", of the circle:
→ C = 2 * (3.14) * (2.76281034802) ;
= (6.28) * (2.76281034802) ;
= 17.3504489856 ;
→ round to: " 17.35 units" .
__________________________________
The answer is: " 17.35 " .
__________________________________
→ The circumference of the circle is: " 17.35 units " .
__________________________________