(a) What is the value of x in the figure given below if it is known that perimeter of the triangle is 86?

(b) Frame an equation for the following case and find the value of the unknown:
In an isosceles triangle, the vertex angle is twice of either base angles. (Let the base angle be b in degrees. Remember that the sum of angles of a triangle is 180 degrees). [3 MARKS]

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Solution

(a) 1 Mark
(b) Framing the equation: 1 Mark
Solution: 1 Mark

(a) Since it is a triangle, the perimeter of a triangle is equal to the sum of all the sides of the triangle.

So, $x + (x + 3) + 41 = 86$

$\Rightarrow 2 x + 44 = 86$

$\Rightarrow 2 x = 42$

$\Rightarrow x = 21$ .

(b) Let the base angle be $b^{\circ}$
Let the vertex angle be $a^{\circ}$
In an isosceles triangle base angles are equal.
$∴ a^{\circ} + b^{\circ} + b^{\circ} = 180^{\circ}$

$2 b^{\circ} + b^{\circ} + b^{\circ} = 180^{\circ} \Rightarrow$ Given that vertex angle is twice the base angle.

$∴ 4 b^{\circ} = 180^{\circ}$

$b^{\circ} = (\frac{180}{4})^{\circ}$

$b^{\circ} = 45^{\circ}$

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(ii) Laxmi’s father is $49$ years old. He is $4$ years older than three times Laxmi’s age. (Take Laxmi’s age to be $y$ years.)

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