Question

in a parallelogram abcd , ab=10and the altitude corresponding to the sides ab and ad are respectively 7cm and 8 cm ,find ad​

Answer 1

Question:

In a parallelogram ABCD , AB = 10 cm and the altitudes corresponding to the sides AB and AD are respectively 7cm and 8 cm , find AD .

Answer:

AD = 8¾ cm OR 8.75 cm

Note:

• A parallelogram is a quadrilateral whose opposite sides are parallel and equal .

• The two diagonals of parallelogram bisect each other.

• The area of a parallelogram = Base•Altitude

Solution:

Let DL be the altitude corresponding to the side AB and BM be the altitude corresponding to the side AD .

According to the question,

The altitudes corresponding to the sides AB and AD are 7cm and 8 cm respectively.

Thus,

DL = 7 cm

BM = 8 cm

Now,

When AB is taken as base and DL is taken as altitude, then the area of parallelogram ABCD will be given as ;

=> Area = AB × DL

=> Area = 10 × 7

=> Area = 70 cm² ------(1)

Also,

When AD is taken as base and BM is taken as altitude, then the area of parallelogram ABCD will be given as ;

=> Area = AD × BM

=> Area = AD × 8

=> Area = 8•AD cm² ------(2)

Now,

From eq-(1) and eq-(2) , we have;

=> 70 = 8•AD

=> AD = 70/8

=> AD = 35/4 cm

=> AD = 8¾ cm

=> AD = 8.75 cm

Hence,

The required value of AD is 8¾ cm OR 8.75 cm

Answer 2

$\Huge{\underline{\boxed{\bf{\red{Answer\::}}}}}$

$\huge{\boxed{\bf{\blue{8.75}}}}$

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

• $\large{\underline{\bf{Given\::}}}$

ABCD is a parallelogram such that AB = CD and AC = BD.

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

Lenght of AD.

So ,

$\rightarrow$ Area of parallelogram = XD × AB

$\rightarrow$ Area of parallelogram = 10 × 7

$\rightarrow$ Area of parallelogram = $\bf{70^{2}cm}$ ....... (1)

Now,

In parallalogram ABCD = AD × 8 ........(2)

From equations 1 and 2 we get.

$\rightarrow$ AD × 8 = 70

$\rightarrow$ AD = 70/8 = $\bf{8.75cm}$

$\rule{300}2$