Question
In a parallelogram ABCD, it is being given that AB = 10cm and the altitudes corresponding to the sides AB and AD are DL = 6cm and BM = 8cm, respectively. Find AD.
✓
Answer
Since ABCD is a parallelogram and DL is perpendicular to AB.
So, its area = AB × DL
= (10 × 6)cm2
= 60cm2
Also, in parallelogram ABCD,
$\text{BM}\perp\text{AD}$
$\therefore$ Area of parallelogram ABCD = AD × BM
60 = AD × 8cm
$\therefore$ AD × 8 = 60
$\Rightarrow\ \text{AD}=\frac{60}{8}=7.5\text{cm}$
$\therefore$ AD = 7.5cm
So, its area = AB × DL
= (10 × 6)cm2
= 60cm2
Also, in parallelogram ABCD,
$\text{BM}\perp\text{AD}$
$\therefore$ Area of parallelogram ABCD = AD × BM
60 = AD × 8cm
$\therefore$ AD × 8 = 60
$\Rightarrow\ \text{AD}=\frac{60}{8}=7.5\text{cm}$
$\therefore$ AD = 7.5cm
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Factorize:
a2x2 + (ax2 + 1)x + a
a2x2 + (ax2 + 1)x + a
If x - 2 is a factor of the following two polynomials, find the values of a in case:
x5 - 3x4 - ax3 + 3ax2 + 2ax + 4
x5 - 3x4 - ax3 + 3ax2 + 2ax + 4
Simplify:
$\frac{1}{\sqrt{3}+\sqrt{2}}-\frac{2}{\sqrt{5}-\sqrt{3}}-\frac{3}{\sqrt{2}-\sqrt{5}}$
→$\frac{1}{\sqrt{3}+\sqrt{2}}-\frac{2}{\sqrt{5}-\sqrt{3}}-\frac{3}{\sqrt{2}-\sqrt{5}}$
Simplify:
$\frac{155\times155\times155-55\times55\times55}{155\times155+155\times55+55\times55}$
→$\frac{155\times155\times155-55\times55\times55}{155\times155+155\times55+55\times55}$
Find the coordinates of the point:
- Which lies on x and y axes both.
- Whose ordinate is -4 and which lies on y-axis.
- whose abscissa is 5 and which lies on x-axis.
The marks of 15 students in an examination are 25, 19, 17, 24, 23, 29, 31, 40, 19, 20, 22, 26, 17, 35, 21.
Find the median score.
Find the median score.
If the temperature of a liquid can be measured in kelvin units as x°K or in fahrenheit units as y°F, the relation between the two systems of measurement of temperature is given by the linear equation.
$\text{y}=\frac{9}{5}(\text{x}-273)+32$
→$\text{y}=\frac{9}{5}(\text{x}-273)+32$
- find the temperature of the liquid in fahrenheit, if the temperature of the liquid is 313K.
- If the temperature is 158°F, then find the temperature in kelvin.
Find the median of:
20, 13, 18, 25, 6, 15, 21, 9, 16, 8, 22
20, 13, 18, 25, 6, 15, 21, 9, 16, 8, 22
The diameter of a copper sphere is 18cm. The sphere is melted and is drawn into a long wire of uniform circular cross-section. If the length of the wire is 108m, find its diameter.
Find the cost of laying grass in a triangular field of sides 50m, 65m and 65m at the rate of Rs. 7 per m2.