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In this page 10th grade geometry worksheet4 we are going to see some
practice questions. You can try the below problems on your own. If you
find it difficult to do any problems you can just click the solution
link to get detailed solution.

(6) In
triangle ABC, AB = AC and BC = 6 cm. D is a point on the side AC such that AD =
5 cm and CD = 4 cm. Show that triangle BCD and triangle ACB are congruent and
hence find BD. Solution

(7) The
points D and E are on the sides AB and AC of triangle ABC respectively, such
that DE and BC are parallel. If AB = 3 AD and the area triangle ABC is 72 cm², then find the area of the quadrilateral DBCE. Solution

(8) The
lengths of the three sides of triangle ABC are 6 cm, 4 cm and 9 cm. Triangle
PQR ad BC are congruent. One of the lengths of the sides of triangle PQR is 35
cm. What is the greatest perimeter possible for triangle PQR Solution

(9) In the
figure, the sides DE and BC are parallel and (AD/B) = 3/5, calculate the value
of

(i) area of
triangle ADE/are of triangle ABC

(ii) area of
trapezium BCED/area of triangle ABC Solution

(10) The
government plans to develop a new industrial zone in an unused portion of land
in a city. Solution

(11) A boy is
designing a diamond shaped kite, as shown in the figure where AE = 16 cm, EC =
81 cm. He wants to use a straight cross bar BD. How long should it be? Solution

(12) A
student wants to determine the height of flag pole. He placed a small mirror on
the ground so that he can see reflection of the top of the flagpole. The
distance of the mirror from him is 0.5 m and the distance of the flagpole from
the mirror is 3 m .If t he eyes are 1.5 m above the ground level, then find the
height of the flagpole (The foot of student, mirror and the foot of flagpole
lie along the a straight line) Solution

(13) A roof
has a cross section as shown in the diagram