Question

the area of a rombus is 40cm².If the length of one diagonalis 10cm,find the length of other diagonal​

Answer 1

Given :

• Area of rhombus = 40cm².
• Length of one diagonal = 10 cm

To find :

• The length of other diagonal.

According to the question,

➞ Area of rhombus = ½ × d₁ × d₂

➞ 40 cm² = ½ × 10 cm × d₂

➞ 40 cm² = 5 cm × d₂

➞ 40 cm² ÷ 5 cm = d₂

➞ 8 cm = d₂

• So,the length of other diagonal is 8 cm.

____________________

❖ Properties of rhombus :

• All sides of a rhombus is equal and parallel to each other.

❖ Some formulas :

• Area of rectangle = Length × Breadth
• Area of square = Side × Side
• Surface area of a cube = 6a²
• Surface area of cuboid = 2(lb + bh + hl)
• Volume of cuboid = l × b × h
• Total surface area of a hemisphere = 3πr²
• Curved surface area of a cone = πrl
• Total surface area of a cylinder = 2πr(r + h)

Answer 2

$\underline{\underline{\textsf{\maltese\:\: Given :}}}$

☞ Area of rhombus = 40cm²

☞ Length of one diagonal = 10cm

$\underline{\underline{\textsf{\maltese\:\: To Find :}}}$

☞ Length of other diagonal = ?

$\underline{\underline{\textsf{\maltese\:\: Diagram :}}}$

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\put(0,0){\line(1,3){1.5}}\put(0,0){\line(1,0){5}}\put(5,0){\line(1,3){1.5}}\put(1.5,4.5){\line(1,0){5}}\qbezier(1.56,4.5)(1.56,4.5)(5,0)\qbezier(6.45,4.5)(6.45,4.5)(0,0)\put(-0.5,-0.5){\sf B}\put(1,4.8){\sf A}\put(5.2,-0.5){\sf C}\put(6.7,4.75){\sf D}\put(3,1.6){\sf O}\put(4,3){\bf10 cm} \put(6,2){\bf {Area =40 \bf{cm}^2 }} \put(7,0){\framebox(2.7,0.6)}\put(7,0){\bf{@ BeBrainliest}}\end{picture}$

$\underline{\underline{\textsf{\maltese\:\: Solution :}}}$

☯︎ Ares of rhombus = $\dfrac{1}{2}$ × Product of diagonals

⇒ Area of rhombus = $\dfrac{1}{2}$ × d₁ × d₂

⇒ 40cm² = $\dfrac{1}{2}$ × AC × DB

⇒ 40cm² = $\dfrac{1}{2}$ × AC × 10cm

⇒ 40cm² × 2 × $\dfrac{1}{10 \sf cm}$ = AC

⇒ 8cm = AC

⇒ AC = 8cm.

∴ Length of other diagonal is 8cm.

$\underline{\underline{\textsf{\maltese\:\: Learn more from Brainly :}}}$

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