Answer
Verified
421.2k+ views
Hint: Area of the rhombus in terms of base and height is given as; $\text{Any side}\times \text{corresponding altitude}$ . Area of rhombus in terms of the diagonals can be given as
Complete step by step answer:
$\dfrac{1}{2}\times {{\left( \text{diagonal} \right)}_{1}}\times {{\left( \text{diagonal} \right)}_{2}}$ use both the identities to get the area of rhombus and equate them to get the unknown diagonal.
Complete step by step answer:
Here, it is given that the length of an altitude on the side of rhombus of length 6.5 cm, is 10 cm. And we need to determine the length of a diagonal if the length of another diagonal is 26 cm. so, we can draw an sketch as
So, let us suppose a Rhombus ABCD with side DC = 6.5 cm and altitude AD is of length 10 cm on it. And we need to determine length BD if AC = 26 cm. We know the area of rhombus can be given two ways. One in form of base and corresponding height and another in terms of both the diagonals. So, both can be given as
Area of rhombus = side $\times $ corresponding altitude
$ \text{Area of rhombus = }\dfrac{1}{2}\times {{\left( \text{diagonal} \right)}_{1}}\times {{\left( \text{diagonal} \right)}_{2}} \\ $
So, area with side DC and AM as a corresponding altitude from the first relation of the area can be given as
Area of rhombus ABCD $=6.5\times 10=65c{{m}^{2}}$
Similarly, area of rhombus with the help of diagonals BD and AC can be given from the second relation as
Area of rhombus ABCD $=\dfrac{1}{2}\times 26\times BD$
So, equating both the areas calculated above, as both are representing the area of rhombus ABCD. Hence we get
65 $=\dfrac{1}{2}\times 26\times BD$
$\dfrac{65}{13}=BD $
$ BD=5cm $
Hence, the length of the other diagonal is 5 cm.
So option (a) is correct.
Recently Updated Pages
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
What organs are located on the left side of your body class 11 biology CBSE
Write an application to the principal requesting five class 10 english CBSE
What is the type of food and mode of feeding of the class 11 biology CBSE
Name 10 Living and Non living things class 9 biology CBSE