Problem 1 :
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 :
From the given information let us draw a rough diagram.
∆ PQR ~ ∆ ABC
PQ/AB = QR/BC = PR/AC = perimeter of ∆ PQR/Perimeter of ∆ BC
Let QR = 35
The corresponding sides must be QR and BC.
Perimeter of ∆ PQR / Perimeter of ∆ ABC is
= QR/BC
= 35/4
Perimeter of triangle PQR = (35/4) ⋅ 19
= 665/4
= 166.25
So, perimeter of triangle PQR is 166.25 cm².
Problem 2 :
In the figure given below, 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 :
In triangle ABC, the sides DE and BC are parallel
Area of ∆ ADE/ Area of ∆ ABC = AD^{2}/AB^{2}
= (3k)^{2}/(8k)^{2}
= 9/64
(ii) Area of ∆ ADE = 9 k
Area of ∆ ADE = 64 k
Area of trapezium BCDE = area of ∆ ABC – area of ∆ ADE
= 64 k – 9 k
= 55 k
Area of trapezium BCDE/Area of ∆ ABC = 55 k/64 k
= 55/64
Problem 3 :
The government plans to develop a new industrial zone in an unused portion of land in a city.
The shaded portion of the map shown given below indicates the area of the new industrial zone. Find the area of the new industrial zone.
Solution :
By considering the lines AD and BC,the angles
∠AEB = ∠DEC (vertically opposite angles)
∠ EAB = ∠EDC (alternate angles)
By using AA similarity criterion ∆ EAB ~ ∆ EDC
(AB/DC) = (EF/EG)
EF = (AB/DC) x EG
= (3/1) x 1.4
= 4.2 km
Area of new industrial zone = Area of ∆ EAB
= (1/2) ⋅ AB ⋅ EF
= (1/2) ⋅ 3 ⋅ 4.2
= 6.3 km²
So, the area of new industrial zone is 6.3 km²
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