The perimeter of an isosceles triangle is 42 cm . Its base is 2 3 times the sum of equal sides. Find the length of each side and the area of the triangle.

Given that, in an isosceles triangle, Perimeter = 42 cm and base = 2 3 × (Sum of equal sides) Let the base be a cm and equal sides be b cm each. As per given, base ⇒ a = 2 3 × 2 b ⇒ 2 b = 3 2 a .........(i) As we know that, Perimeter of the isosceles triangle = base + (sum of the two equal sides) ⇒ a + 2 b = 42 cm ⇒ a + 3 2 a = 42 cm ⇒ 5 2 a = 42 cm ⇒ a = 42 × 2 5 = 84 5 cm ⇒ a = 16 . 8 cm From equation (i), we have, ⇒ b = 3 4 a = 3 4 × 16 . 8 = 3 × 4 . 2 cm ⇒ b = 12 . 6 cm Then, area of an isosceles triangle = 1 4 × a × 4 b 2 - a 2 = 1 4 × 16 . 8 × 4 × ( 12 . 6 ) 2 - ( 16 . 8 ) 2 cm 2 = 1 4 × 16 . 8 × 635 . 04 - 282 . 24 cm 2 = 882 5 25 cm 2 = 78 . 89 cm 2 Hence, required area of the triangle is 78 . 89 cm 2 .

E M B I B E

ICSE Mathematics>Mensuration>Chapter 16 - Area of Plane Figures>Exercise

O P Malhotra, S K Gupta and, Anubhuti Gangal Solutions for Exercise 2: Exercise

Author:O P Malhotra, S K Gupta & Anubhuti Gangal

O P Malhotra Mathematics Solutions for Exercise - O P Malhotra, S K Gupta and, Anubhuti Gangal Solutions for Exercise 2: Exercise

Attempt the practice questions from Exercise 2: Exercise with hints and solutions to strengthen your understanding. ICSE Mathematics solutions are prepared by Experienced Embibe Experts.

Questions from O P Malhotra, S K Gupta and, Anubhuti Gangal Solutions for Exercise 2: Exercise with Hints & Solutions

EASY

9th ICSE

IMPORTANT

ICSE Mathematics>Chapter 16 - Area of Plane Figures>Exercise>Q 1

For a triangle, find:

Base	$8 cm$
Height	$14 cm$
Area	$. . . . {cm}^{2}$

EASY

9th ICSE

IMPORTANT

ICSE Mathematics>Chapter 16 - Area of Plane Figures>Exercise>Q 1

For a triangle, find area.

Base	$5 cm$
Height	$20 cm$
Area	$. . . . . . {cm}^{2}$

EASY

9th ICSE

IMPORTANT

ICSE Mathematics>Chapter 16 - Area of Plane Figures>Exercise>Q 1

For a triangle if

Base	$x cm$
Height	$2 x cm$
Area	$x^{k}$ ${cm}^{2}$

Then find the value of $k$ .

EASY

9th ICSE

IMPORTANT

ICSE Mathematics>Chapter 16 - Area of Plane Figures>Exercise>Q 1

For a triangle, find:

Base	$6 cm$
Height	$. . . . . cm$
Area	$30 {cm}^{2}$

EASY

9th ICSE

IMPORTANT

ICSE Mathematics>Chapter 16 - Area of Plane Figures>Exercise>Q 1

For a triangle, find:

Base	$. . . . cm$
Height	$5 cm$
Area	$50 {cm}^{2}$

EASY

9th ICSE

IMPORTANT

ICSE Mathematics>Chapter 16 - Area of Plane Figures>Exercise>Q 1

For a triangle, find( in $cm$ )

Base	?
Height	$11 cm$
Area	$110 {cm}^{2}$

HARD

9th ICSE

IMPORTANT

ICSE Mathematics>Chapter 16 - Area of Plane Figures>Exercise>Q 17

Find the base of an isosceles triangle whose area is $12 {cm}^{2}$ and one of the equal sides is $5 cm$ ?

HARD

9th ICSE

IMPORTANT

ICSE Mathematics>Chapter 16 - Area of Plane Figures>Exercise>Q 18

The perimeter of an isosceles triangle is $42 cm$ . Its base is $\frac{2}{3}$ times the sum of equal sides. Find the length of each side and the area of the triangle.

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